SherbyNet - /page/wikibook/entry.mu

Micron Document

<!DOCTYPE html>

<title>System dynamics</title>

</head>

<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">System dynamics</span></span>

</h1>

</header>

<p><b>System dynamics</b> (<b>SD</b>) is an approach to understanding the <a href="Nonlinearity" class="mw-redirect" title="Nonlinearity">nonlinear</a> behaviour of <a href="Complex_system" title="Complex system">complex systems</a> over time using <a href="Stock_and_flow" title="Stock and flow">stocks, flows</a>, internal <a href="Feedback_loop" class="mw-redirect" title="Feedback loop">feedback loops</a>, table functions and time delays.<sup id="cite_ref-sysdyn_1-0" class="reference"><a href="#cite_note-sysdyn-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2></div>

<p>System dynamics is a <a href="Methodology" title="Methodology">methodology</a> and <a href="Mathematical_model" title="Mathematical model">mathematical modeling</a> technique to frame, understand, and discuss complex issues and problems. Originally developed in the 1950s to help corporate managers improve their understanding of industrial processes, SD is currently being used throughout the public and private sector for policy analysis and design.<sup id="cite_ref-UDE_2-0" class="reference"><a href="#cite_note-UDE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>Convenient <a href="Graphical_user_interface" title="Graphical user interface">graphical user interface</a> (GUI) system dynamics software developed into user friendly versions by the 1990s and have been applied to diverse systems. SD models solve the problem of simultaneity (mutual causation) by updating all variables in small time increments with positive and negative feedbacks and time delays structuring the interactions and control. The best known SD model is probably the 1972 <i><a href="The_Limits_to_Growth" title="The Limits to Growth">The Limits to Growth</a></i>. This model forecast that exponential growth of population and capital, with finite resource sources and sinks and perception delays, would lead to economic collapse during the 21st century under a wide variety of growth scenarios.

</p><p>System dynamics is an aspect of <a href="Systems_theory" title="Systems theory">systems theory</a> as a method to understand the dynamic behavior of complex systems. The basis of the method is the recognition that the structure of any system, the many circular, interlocking, sometimes time-delayed relationships among its components, is often just as important in determining its behavior as the individual components themselves. Examples are <a href="Chaos_theory" title="Chaos theory">chaos theory</a> and <a href="Social_dynamics" title="Social dynamics">social dynamics</a>. It is also claimed that because there are often properties-of-the-whole which cannot be found among the properties-of-the-elements, in some cases the behavior of the whole cannot be explained in terms of the behavior of the parts.

</p>

<div class="mw-heading mw-heading2"><h2 id="History">History</h2></div>

<p>System dynamics was created during the mid-1950s<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> by Professor <a href="Jay_Forrester" class="mw-redirect" title="Jay Forrester">Jay Forrester</a> of the <a href="Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a>. In 1956, Forrester accepted a professorship in the newly formed <a href="MIT_Sloan_School_of_Management" title="MIT Sloan School of Management">MIT Sloan School of Management</a>. His initial goal was to determine how his background in science and engineering could be brought to bear, in some useful way, on the core issues that determine the success or failure of corporations. Forrester's insights into the common foundations that underlie engineering, which led to the creation of system dynamics, were triggered, to a large degree, by his involvement with managers at <a href="General_Electric" title="General Electric">General Electric</a> (GE) during the mid-1950s. At that time, the managers at GE were perplexed because employment at their appliance plants in Kentucky exhibited a significant three-year cycle. The <a href="Business_cycle" title="Business cycle">business cycle</a> was judged to be an insufficient explanation for the employment instability. From hand simulations (or calculations) of the stock-flow-feedback structure of the GE plants, which included the existing corporate decision-making structure for hiring and layoffs, Forrester was able to show how the instability in GE employment was due to the internal structure of the firm and not to an external force such as the business cycle. These hand simulations were the start of the field of system dynamics.<sup id="cite_ref-UDE_2-1" class="reference"><a href="#cite_note-UDE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>During the late 1950s and early 1960s, Forrester and a team of graduate students moved the emerging field of system dynamics from the hand-simulation stage to the formal <a href="Computer_modeling" class="mw-redirect" title="Computer modeling">computer modeling</a> stage. Richard Bennett created the first system dynamics computer modeling language called SIMPLE (Simulation of Industrial Management Problems with Lots of Equations) in the spring of 1958. In 1959, <a href="Phyllis_Fox" title="Phyllis Fox">Phyllis Fox</a> and Alexander Pugh wrote the first version of

<a href="DYNAMO_(programming_language)" title="DYNAMO (programming language)">DYNAMO</a> (DYNAmic MOdels), an improved version of SIMPLE, and the system dynamics language became the industry standard for over thirty years. Forrester published the first, and still classic, book in the field titled <i>Industrial Dynamics</i> in 1961.<sup id="cite_ref-UDE_2-2" class="reference"><a href="#cite_note-UDE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p><p>From the late 1950s to the late 1960s, system dynamics was applied almost exclusively to corporate/managerial problems. In 1968, however, an unexpected occurrence caused the field to broaden beyond corporate modeling. <a href="John_F._Collins" title="John F. Collins">John F. Collins</a>, the former mayor of Boston, was appointed a visiting professor of Urban Affairs at MIT. The result of the Collins-Forrester collaboration was a book titled <i>Urban Dynamics</i>. The <a href="Urban_Dynamics" class="mw-redirect" title="Urban Dynamics">Urban Dynamics</a> model presented in the book was the first major non-corporate application of system dynamics.<sup id="cite_ref-UDE_2-3" class="reference"><a href="#cite_note-UDE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> In 1967, <a href="Richard_M._Goodwin" title="Richard M. Goodwin">Richard M. Goodwin</a> published the first edition of his paper "A Growth Cycle",<sup id="cite_ref-GROWTH_4-0" class="reference"><a href="#cite_note-GROWTH-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> which was the first attempt to apply the principles of system dynamics to economics. He devoted most of his life teaching what he called "Economic Dynamics", which could be considered a precursor of modern <a href="Non-equilibrium_economics" title="Non-equilibrium economics">Non-equilibrium economics</a>.<sup id="cite_ref-GOODWIN_5-0" class="reference"><a href="#cite_note-GOODWIN-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>

</p><p>The second major noncorporate application of system dynamics came shortly after the first. In 1970, Jay Forrester was invited by the <a href="Club_of_Rome" title="Club of Rome">Club of Rome</a> to a meeting in Bern, Switzerland. The Club of Rome is an organization devoted to solving what its members describe as the "predicament of mankind"—that is, the global crisis that may appear sometime in the future, due to the demands being placed on the Earth's <a href="Carrying_capacity" title="Carrying capacity">carrying capacity</a> (its sources of renewable and nonrenewable resources and its sinks for the disposal of pollutants) by the world's exponentially growing population. At the Bern meeting, Forrester was asked if system dynamics could be used to address the predicament of mankind. His answer, of course, was that it could. On the plane back from the Bern meeting, Forrester created the first draft of a system dynamics model of the world's socioeconomic system. He called this model WORLD1. Upon his return to the United States, Forrester refined WORLD1 in preparation for a visit to MIT by members of the Club of Rome. Forrester called the refined version of the model WORLD2. Forrester published WORLD2 in a book titled <a href="World_Dynamics" class="mw-redirect" title="World Dynamics">World Dynamics</a>.<sup id="cite_ref-UDE_2-4" class="reference"><a href="#cite_note-UDE-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading2"><h2 id="Topics_in_systems_dynamics">Topics in systems dynamics</h2></div>

<p>The primary elements of system dynamics diagrams are feedback, accumulation of flows into stocks and time delays.

</p><p>As an illustration of the use of system dynamics, imagine an organisation that plans to introduce an innovative new durable consumer product. The organisation needs to understand the possible market dynamics in order to design marketing and production plans.

</p>

<div class="mw-heading mw-heading3"><h3 id="Causal_loop_diagrams">Causal loop diagrams</h3></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Causal_loop_diagram" title="Causal loop diagram">Causal loop diagram</a></div>

<p>In the system dynamics methodology, a problem or a system (e.g., ecosystem, political system or mechanical system) may be represented as a <a href="Causal_loop_diagram" title="Causal loop diagram">causal loop diagram</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> A causal loop diagram is a simple map of a system with all its constituent components and their interactions. By capturing interactions and consequently the feedback loops (see figure below), a causal loop diagram reveals the structure of a system. By understanding the structure of a system, it becomes possible to ascertain a system's behavior over a certain time period.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>

</p><p>The causal loop diagram of the new product introduction may look as follows:

</p>

<p>There are two feedback loops in this diagram. The positive reinforcement (labeled R) loop on the right indicates that the more people have already adopted the new product, the stronger the word-of-mouth impact. There will be more references to the product, more demonstrations, and more reviews. This positive feedback should generate sales that continue to grow.

</p><p>The second feedback loop on the left is negative reinforcement (or "balancing" and hence labeled B). Clearly, growth cannot continue forever, because as more and more people adopt, there remain fewer and fewer potential adopters.

</p><p>Both feedback loops act simultaneously, but at different times they may have different strengths. Thus one might expect growing sales in the initial years, and then declining sales in the later years. However, in general a causal loop diagram does not specify the structure of a system sufficiently to permit determination of its behavior from the visual representation alone.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Stock_and_flow_diagrams">Stock and flow diagrams</h3></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Stock_and_flow" title="Stock and flow">Stock and flow</a></div>

<p>Causal loop diagrams aid in visualizing a system's structure and behavior, and analyzing the system qualitatively. To perform a more detailed quantitative analysis, a causal loop diagram is transformed to a <a href="Stock_and_flow" title="Stock and flow">stock and flow</a> diagram. A stock and flow model helps in studying and analyzing the system in a quantitative way; such models are usually built and simulated using computer software.

</p><p>A stock is the term for any entity that accumulates or depletes over time. A flow is the rate of change in a stock.

</p>

<p>In this example, there are two stocks: Potential adopters and Adopters. There is one flow: New adopters. For every new adopter, the stock of potential adopters declines by one, and the stock of adopters increases by one.

</p>

<div class="mw-heading mw-heading3"><h3 id="Equations">Equations</h3></div>

<p>The real power of system dynamics is utilised through simulation. Although it is possible to perform the modeling in a <a href="Spreadsheet" title="Spreadsheet">spreadsheet</a>, there are a <a href="Comparison_of_system_dynamics_software" title="Comparison of system dynamics software">variety of software</a> packages that have been optimised for this.

</p><p>The steps involved in a simulation are:

</p>

<ul><li>Define the problem boundary.</li>

<li>Identify the most important stocks and flows that change these stock levels.</li>

<li>Identify sources of information that impact the flows.</li>

<li>Identify the main feedback loops.</li>

<li>Draw a causal loop diagram that links the stocks, flows and sources of information.</li>

<li>Write the equations that determine the flows.</li>

<li>Estimate the parameters and initial conditions. These can be estimated using statistical methods, expert opinion, market research data or other relevant sources of information.<sup id="cite_ref-Sterman2001CMR_9-0" class="reference"><a href="#cite_note-Sterman2001CMR-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li>

<li>Simulate the model and analyse results.</li></ul>

<p>In this example, the equations that change the two stocks via the flow are:

</p>

<mtext>Potential adopters</mtext>

</mstyle>

</mrow>

</mrow>

</mrow>

</msubsup>

<mtext>New adopters </mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ {\mbox{Potential adopters}}=-\int _{0}^{t}{\mbox{New adopters }}\,dt}</annotation>

</semantics>

</math></span><img src="./7dec771a1eb1abb48013553b40379ce51bdc9865.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:44.875ex; height:6.176ex;" alt="{\displaystyle \ {\mbox{Potential adopters}}=-\int _{0}^{t}{\mbox{New adopters }}\,dt}" loading="lazy"></span>

<mtext>Adopters</mtext>

</mstyle>

</mrow>

</mrow>

</mrow>

</msubsup>

<mtext>New adopters </mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ {\mbox{Adopters}}=\int _{0}^{t}{\mbox{New adopters }}\,dt}</annotation>

</semantics>

</math></span><img src="./84f00dadc726c4ff58fc8a9185265902be02d61b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:33.344ex; height:6.176ex;" alt="{\displaystyle \ {\mbox{Adopters}}=\int _{0}^{t}{\mbox{New adopters }}\,dt}" loading="lazy"></span>

</pre>

<div class="mw-heading mw-heading3"><h3 id="Equations_in_discrete_time">Equations in discrete time</h3></div>

<p>List of all the equations in <a href="Discrete_time" class="mw-redirect" title="Discrete time">discrete time</a>, in their order of execution in each year, for years 1 to 15 :

</p>

<mtext>Probability that contact has not yet adopted</mtext>

</mstyle>

</mrow>

<mtext>Potential adopters</mtext>

</mstyle>

</mrow>

</mrow>

<mtext>Potential adopters </mtext>

</mstyle>

</mrow>

<mtext> Adopters</mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 1)\ {\mbox{Probability that contact has not yet adopted}}={\mbox{Potential adopters}}/({\mbox{Potential adopters }}+{\mbox{ Adopters}})}</annotation>

</semantics>

</math></span><img src="./15f6ff869c65a8c88b6f6831a3515e624961d64a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:103.909ex; height:2.843ex;" alt="{\displaystyle 1)\ {\mbox{Probability that contact has not yet adopted}}={\mbox{Potential adopters}}/({\mbox{Potential adopters }}+{\mbox{ Adopters}})}" loading="lazy"></span>

<mtext>Imitators</mtext>

</mstyle>

</mrow>

<mtext>Adopters</mtext>

</mstyle>

</mrow>

<mtext>Probability that contact has not yet adopted</mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2)\ {\mbox{Imitators}}=q\cdot {\mbox{Adopters}}\cdot {\mbox{Probability that contact has not yet adopted}}}</annotation>

</semantics>

</math></span><img src="./fefa10b75559bb64eb6bc1ba42cb8ed65204de37.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:73.566ex; height:2.843ex;" alt="{\displaystyle 2)\ {\mbox{Imitators}}=q\cdot {\mbox{Adopters}}\cdot {\mbox{Probability that contact has not yet adopted}}}" loading="lazy"></span>

<mtext>Innovators</mtext>

</mstyle>

</mrow>

<mtext>Potential adopters</mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 3)\ {\mbox{Innovators}}=p\cdot {\mbox{Potential adopters}}}</annotation>

</semantics>

</math></span><img src="./5e58b8add1c194d1ccfeb3ec9dae694ab73edcba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.058ex; height:2.843ex;" alt="{\displaystyle 3)\ {\mbox{Innovators}}=p\cdot {\mbox{Potential adopters}}}" loading="lazy"></span>

<mtext>New adopters</mtext>

</mstyle>

</mrow>

<mtext>Innovators</mtext>

</mstyle>

</mrow>

<mtext>Imitators</mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 4)\ {\mbox{New adopters}}={\mbox{Innovators}}+{\mbox{Imitators}}}</annotation>

</semantics>

</math></span><img src="./79365272120b719e52461faff512c0979526399d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.552ex; height:2.843ex;" alt="{\displaystyle 4)\ {\mbox{New adopters}}={\mbox{Innovators}}+{\mbox{Imitators}}}" loading="lazy"></span>

<mtext>Potential adopters</mtext>

</mstyle>

</mrow>

<mtext>New adopters </mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 4.1)\ {\mbox{Potential adopters}}\ -={\mbox{New adopters }}}</annotation>

</semantics>

</math></span><img src="./826b95ebcf4297324b9f7e4f94c0dbc959342891.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.825ex; height:2.843ex;" alt="{\displaystyle 4.1)\ {\mbox{Potential adopters}}\ -={\mbox{New adopters }}}" loading="lazy"></span>

<mtext>Adopters</mtext>

</mstyle>

</mrow>

<mtext>New adopters </mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 4.2)\ {\mbox{Adopters}}\ +={\mbox{New adopters }}}</annotation>

</semantics>

</math></span><img src="./2c0d4446076a3d0c528b8a3f558d580ac1f109be.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.49ex; height:2.843ex;" alt="{\displaystyle 4.2)\ {\mbox{Adopters}}\ +={\mbox{New adopters }}}" loading="lazy"></span>

</pre>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ p=0.03}</annotation>

</semantics>

</math></span><img src="./9732f34c2a160614ddcd42cacd735b1afefbb9a0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.983ex; height:2.509ex;" alt="{\displaystyle \ p=0.03}" loading="lazy"></span>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ q=0.4}</annotation>

</semantics>

</math></span><img src="./333410b559ab0c9d4b661cbc1d5b3f0e59ef2c4d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.72ex; height:2.509ex;" alt="{\displaystyle \ q=0.4}" loading="lazy"></span>

</pre>

<div class="mw-heading mw-heading4"><h4 id="Dynamic_simulation_results">Dynamic simulation results</h4></div>

<div role="note" class="hatnote navigation-not-searchable">Main article: <a href="Dynamic_simulation" class="mw-redirect" title="Dynamic simulation">Dynamic simulation</a></div>

<p>The dynamic simulation results show that the behaviour of the system would be to have growth in <i>adopters</i> that follows a classic s-curve shape.<br>

The increase in <i>adopters</i> is very slow initially, then exponential growth for a period, followed ultimately by saturation.

</p>

<div class="mw-heading mw-heading3"><h3 id="Equations_in_continuous_time">Equations in continuous time</h3></div>

<p>To get intermediate values and better accuracy, the model can run in continuous time: we multiply the number of units of time and we proportionally divide values that change stock levels. In this example we multiply the 15 years by 4 to obtain 60 quarters, and we divide the value of the flow by 4.<br>

Dividing the value is the simplest with the <a href="Euler_method" title="Euler method">Euler method</a>, but other methods could be employed instead, such as <a href="Runge%E2%80%93Kutta_methods" title="Runge–Kutta methods">Runge–Kutta methods</a>.

</p><p>List of the equations in continuous time for trimesters = 1 to 60 :

</p>

<ul><li>They are the same equations as in the section <i>Equation in discrete time</i> above, except equations <i>4.1</i> and <i>4.2</i> replaced by following :</li></ul>

<mtext>Valve New adopters</mtext>

</mstyle>

</mrow>

<mtext>New adopters</mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 10)\ {\mbox{Valve New adopters}}\ ={\mbox{New adopters}}\cdot TimeStep}</annotation>

</semantics>

</math></span><img src="./54b1c272a40acbe2565faa12f431f2c7d5ced7e7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:53.134ex; height:2.843ex;" alt="{\displaystyle 10)\ {\mbox{Valve New adopters}}\ ={\mbox{New adopters}}\cdot TimeStep}" loading="lazy"></span>

<mtext>Potential adopters</mtext>

</mstyle>

</mrow>

<mtext>Valve New adopters</mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 10.1)\ {\mbox{Potential adopters}}\ -={\mbox{Valve New adopters}}}</annotation>

</semantics>

</math></span><img src="./50fc685b06ed0f19722e5723784afbdd7b5862c2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:49.8ex; height:2.843ex;" alt="{\displaystyle 10.1)\ {\mbox{Potential adopters}}\ -={\mbox{Valve New adopters}}}" loading="lazy"></span>

<mtext>Adopters</mtext>

</mstyle>

</mrow>

<mtext>Valve New adopters </mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 10.2)\ {\mbox{Adopters}}\ +={\mbox{Valve New adopters }}}</annotation>

</semantics>

</math></span><img src="./d270260aa025c9e60ee49070e4f0cadefe8cce9a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.045ex; height:2.843ex;" alt="{\displaystyle 10.2)\ {\mbox{Adopters}}\ +={\mbox{Valve New adopters }}}" loading="lazy"></span>

</pre>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ TimeStep=1/4}</annotation>

</semantics>

</math></span><img src="./6d998182e6a8b37e2702d056e1cbc4d5f51e97c1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.321ex; height:2.843ex;" alt="{\displaystyle \ TimeStep=1/4}" loading="lazy"></span>

</pre>

<ul><li>In the below stock and flow diagram, the intermediate flow 'Valve New adopters' calculates the equation :</li></ul>

<mtext>Valve New adopters</mtext>

</mstyle>

</mrow>

<mtext>New adopters </mtext>

</mstyle>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ {\mbox{Valve New adopters}}\ ={\mbox{New adopters }}\cdot TimeStep}</annotation>

</semantics>

</math></span><img src="./f863a70f2e382a73083d495b326dae33711f7799.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:50.485ex; height:2.509ex;" alt="{\displaystyle \ {\mbox{Valve New adopters}}\ ={\mbox{New adopters }}\cdot TimeStep}" loading="lazy"></span>

</pre>

<div class="mw-heading mw-heading2"><h2 id="Application">Application</h2></div>

<p>System dynamics has found application in a wide range of areas, for example <a href="Population_dynamics" title="Population dynamics">population</a>, agriculture,<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <a href="Compartmental_models_in_epidemiology" class="mw-redirect" title="Compartmental models in epidemiology"> epidemiological</a>, <a href="Ecosystem_model" title="Ecosystem model">ecological</a> and <a href="Economics" title="Economics">economic</a> systems, which usually interact strongly with each other.

</p><p>System dynamics have various "back of the envelope" management applications. They are a potent tool to:

</p>

<ul><li>Teach <a href="System_thinking" class="mw-redirect" title="System thinking">system thinking</a> reflexes to persons being coached</li>

<li>Analyze and compare assumptions and <a href="Mental_model" title="Mental model">mental models</a> about the way things work</li>

<li>Gain qualitative insight into the workings of a system or the consequences of a decision</li>

<li>Recognize archetypes of dysfunctional systems in everyday practice</li></ul>

<p>Computer software is used to <a href="Computer_simulation" title="Computer simulation">simulate</a> a system dynamics <a href="Model_(abstract)" class="mw-redirect" title="Model (abstract)">model</a> of the situation being studied. Running "what if" simulations to test certain policies on such a model can greatly aid in understanding how the system changes over time. System dynamics is very similar to <a href="Systems_thinking" title="Systems thinking">systems thinking</a> and constructs the same <a href="Causal_loop_diagram" title="Causal loop diagram">causal loop diagrams</a> of systems with feedback. However, system dynamics typically goes further and utilises simulation to study the behaviour of systems and the impact of alternative policies.<sup id="cite_ref-SysDynSociety_11-0" class="reference"><a href="#cite_note-SysDynSociety-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>

</p><p>System dynamics has been used to investigate resource dependencies, and resulting problems, in product development.<sup id="cite_ref-Repenning:2001kx_12-0" class="reference"><a href="#cite_note-Repenning:2001kx-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Repenning:1999ng_13-0" class="reference"><a href="#cite_note-Repenning:1999ng-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>

</p><p>A system dynamics approach to <a href="Macroeconomics" title="Macroeconomics">macroeconomics</a>, known as <i><a href="Minsky_(economic_simulator)" class="mw-redirect" title="Minsky (economic simulator)">Minsky</a></i>, has been developed by the economist <a href="Steve_Keen" title="Steve Keen">Steve Keen</a>.<sup id="cite_ref-SForge_14-0" class="reference"><a href="#cite_note-SForge-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> This has been used to successfully model world economic behaviour from the apparent stability of the <a href="Great_Moderation" title="Great Moderation">Great Moderation</a> to the <a href="2008_financial_crisis" title="2008 financial crisis">2008 financial crisis</a>.

</p>

<div class="mw-heading mw-heading3"><h3 id="Example:_Growth_and_decline_of_companies">Example: Growth and decline of companies</h3></div>

<p>The figure above is a causal loop diagram of a system dynamics model created to examine forces that may be responsible for the growth or decline of <a href="Life_insurance" title="Life insurance">life insurance</a> companies in the <a href="United_Kingdom" title="United Kingdom">United Kingdom</a>. A number of this figure's features are worth mentioning. The first is that the model's negative feedback loops are identified by <i>C's</i>, which stand for <i>Counteracting</i> loops. The second is that double slashes are used to indicate places where there is a significant delay between causes (i.e., variables at the tails of arrows) and effects (i.e., variables at the heads of arrows). This is a common causal loop diagramming convention in system dynamics. Third, is that thicker lines are used to identify the feedback loops and links that author wishes the audience to focus on. This is also a common system dynamics diagramming convention. Last, it is clear that a decision maker would find it impossible to think through the dynamic behavior inherent in the model, from inspection of the figure alone.<sup id="cite_ref-Tay_Feedback_15-1" class="reference"><a href="#cite_note-Tay_Feedback-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>

</p>

<div class="mw-heading mw-heading3"><h3 id="Example:_Piston_motion">Example: Piston motion</h3></div>

<ol><li>Objective: study of a crank-connecting rod system.<br> We want to model a crank-connecting rod system through a system dynamic model. Two different full descriptions of the physical system with related systems of equations can be found <a href="Piston_motion_equations#Position" title="Piston motion equations">here</a> <span class="languageicon">(in English)</span> and <a href="https://fr.wikipedia.org/wiki/Syst%C3%A8me_bielle-manivelle#Équations_horaires" class="extiw external" title="fr:Système bielle-manivelle">here</a> <span class="languageicon">(in French)</span>; they give the same results. In this example, the crank, with variable radius and angular frequency, will drive a piston with a variable connecting rod length.</li>

<li>System dynamic modeling: the system is now modeled, according to a stock and flow system dynamic logic.<br> The figure below shows the stock and flow diagram </li>

<li>Simulation: the behavior of the crank-connecting rod dynamic system can then be simulated.<br> The next figure is a 3D simulation created using <a href="Procedural_animation" title="Procedural animation">procedural animation</a>. Variables of the model animate all parts of this animation: crank, radius, angular frequency, rod length, and piston position.</li></ol>

/* start https://en.wikipedia.org/ */

.mw-parser-output .col-begin{border-collapse:collapse;padding:0;color:inherit;width:100%;border:0;margin:0}.mw-parser-output .col-begin-small{font-size:90%}.mw-parser-output .col-break{vertical-align:top;text-align:left}.mw-parser-output .col-break-2{width:50%}.mw-parser-output .col-break-3{width:33.3%}.mw-parser-output .col-break-4{width:25%}.mw-parser-output .col-break-5{width:20%}@media(max-width:720px){.mw-parser-output .col-begin,.mw-parser-output .col-begin>tbody,.mw-parser-output .col-begin>tbody>tr,.mw-parser-output .col-begin>tbody>tr>td{display:block!important;width:100%!important}.mw-parser-output .col-break{padding-left:0!important}}

/* end https://en.wikipedia.org/ */

</style><div>

<dl><dt>Related subjects</dt></dl>

<ul><li><a href="Causal_loop_diagram" title="Causal loop diagram">Causal loop diagram</a></li>

<li><a href="Comparison_of_system_dynamics_software" title="Comparison of system dynamics software">Comparison of system dynamics software</a></li>

<li><a href="Ecosystem_model" title="Ecosystem model">Ecosystem model</a></li>

<li><a href="Plateau_Principle" class="mw-redirect" title="Plateau Principle">Plateau Principle</a></li>

<li><a href="System_archetype" title="System archetype">System archetypes</a></li>

<li><a href="System_Dynamics_Society" title="System Dynamics Society">System Dynamics Society</a></li>

<li><a href="Twelve_leverage_points" title="Twelve leverage points">Twelve leverage points</a></li>

<li><a href="Wicked_problem" title="Wicked problem">Wicked problems</a></li>

<li><a href="World3" title="World3">World3</a></li>

<li><a href="Population_dynamics" title="Population dynamics">Population dynamics</a></li>

<li><a href="Predator-prey_interaction" class="mw-redirect" title="Predator-prey interaction">Predator-prey interaction</a></li></ul>

</td>

<dl><dt>Related fields</dt></dl>

<ul><li><a href="Dynamical_systems_theory" title="Dynamical systems theory">Dynamical systems theory</a></li>

<li><a href="Grey_box_model" title="Grey box model">Grey box model</a></li>

<li><a href="Operations_research" title="Operations research">Operations research</a></li>

<li><a href="Social_dynamics" title="Social dynamics">Social dynamics</a></li>

<li><a href="System_identification" title="System identification">System identification</a></li>

<li><a href="Systems_theory" title="Systems theory">Systems theory</a></li>

<li><a href="Systems_thinking" title="Systems thinking">Systems thinking</a></li>

<li><a href="Cybernetics" title="Cybernetics">Cybernetics</a></li>

</td>

<dl><dt>Related scientists</dt></dl>

<ul><li><a href="Jay_Forrester" class="mw-redirect" title="Jay Forrester">Jay Forrester</a></li>

<li><a href="Dennis_Meadows" title="Dennis Meadows">Dennis Meadows</a></li>

<li><a href="Donella_Meadows" title="Donella Meadows">Donella Meadows</a></li>

<li><a href="Peter_Senge" title="Peter Senge">Peter Senge</a></li>

<li><a href="Graeme_Snooks" title="Graeme Snooks">Graeme Snooks</a></li>

<li><a href="John_Sterman" title="John Sterman">John Sterman</a></li></ul>

</td>

/* start https://en.wikipedia.org/ */

.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}

/* end https://en.wikipedia.org/ */

</style>

<p>

</p>

</td></tr></tbody></table></div>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}

/* end https://en.wikipedia.org/ */

</style><div class="reflist">

/* start https://en.wikipedia.org/ */

.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("./mw/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("./mw/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("./mw/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("./mw/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}

/* end https://en.wikipedia.org/ */

</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.mit.edu/sysdyn/sd-intro/">"MIT System Dynamics in Education Project (SDEP)"</a>.</cite></span>

</li>

<li id="cite_note-UDE-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-UDE_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-UDE_2-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-UDE_2-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-UDE_2-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-UDE_2-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text">Michael J. Radzicki and Robert A. Taylor (2008). <a rel="nofollow" class="external text" href="http://www.systemdynamics.org/DL-IntroSysDyn/start.htm">"Origin of System Dynamics: Jay W. Forrester and the History of System Dynamics"</a>. In: <i>U.S. Department of Energy's Introduction to System Dynamics</i>. Retrieved 23 October 2008.</span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Forrester, Jay (1971). Counterintuitive behavior of social systems. Technology Review 73(3): 52–68</span>

</li>

<li id="cite_note-GROWTH-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-GROWTH_4-0">^</a></b></span> <span class="reference-text">Goodwin, R.M. (1982). A Growth Cycle. In: Essays in Economic Dynamics. Palgrave Macmillan, London. <a rel="nofollow" class="external autonumber" href="https://doi.org/10.1007/978-1-349-05504-3_12">[1]</a></span>

</li>

<li id="cite_note-GOODWIN-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-GOODWIN_5-0">^</a></b></span> <span class="reference-text">Di Matteo, M., & Sordi, S. (2015). Goodwin in Siena: economist, social philosopher and artist. Cambridge Journal of Economics, 39(6), 1507–1527. <a rel="nofollow" class="external autonumber" href="http://www.jstor.org/stable/24695947">[2]</a></span>

</li>

<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFSterman2000" class="citation book cs1">Sterman, John D. (2000). <i>Business Dynamics: Systems Thinking and Modeling for a Complex World</i>. Boston: McGraw-Hill. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>0-07-231135-5</bdi>.</cite></span>

</li>

<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Meadows, Donella. (2008). Thinking in Systems: A Primer. Earthscan</span>

</li>

<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><cite id="CITEREFRichardson1986" class="citation journal cs1">Richardson, G. P. (1986). "Problems with causal-loop diagrams". <i>Syst. Dyn. Rev</i>. <b>2</b> (2): <span class="nowrap">158–</span>170. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fsdr.4260020207">10.1002/sdr.4260020207</a>.</cite></span>

</li>

<li id="cite_note-Sterman2001CMR-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Sterman2001CMR_9-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFSterman2001" class="citation journal cs1">Sterman, John D. (2001). "System dynamics modeling: Tools for learning in a complex world". <i>California Management Review</i>. <b>43</b> (4): <span class="nowrap">8–</span>25. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F41166098">10.2307/41166098</a>. <a href="JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/41166098">41166098</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4637381">4637381</a>.</cite></span>

</li>

<li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">F. H. A. Rahim, N. N. Hawari and N. Z. Abidin, "Supply and demand of rice in Malaysia: A system dynamics approach", International Journal of Supply Chain and Management, Vol.6, No.4, pp. 234-240, 2017.</span>

</li>

<li id="cite_note-SysDynSociety-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-SysDynSociety_11-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.systemdynamics.org/">System Dynamics Society</a></span>

</li>

<li id="cite_note-Repenning:2001kx-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-Repenning:2001kx_12-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFRepenning2001" class="citation journal cs1">Repenning, Nelson P. (2001). <a rel="nofollow" class="external text" href="https://dspace.mit.edu/bitstream/1721.1/3961/2/Tilting_v40-web.pdf">"Understanding fire fighting in new product development"</a> <span class="cs1-format">(PDF)</span>. <i>The Journal of Product Innovation Management</i>. <b>18</b> (5): <span class="nowrap">285–</span>300. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0737-6782%2801%2900099-6">10.1016/S0737-6782(01)00099-6</a>. <a href="Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/1721.1%2F3961">1721.1/3961</a></span>.</cite></span>

</li>

<li id="cite_note-Repenning:1999ng-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Repenning:1999ng_13-0">^</a></b></span> <span class="reference-text">Nelson P. Repenning (1999). <i>Resource dependence in product development improvement efforts</i>, <a href="MIT_Sloan_School_of_Management" title="MIT Sloan School of Management">MIT Sloan School of Management</a> Department of Operations Management/System Dynamics Group, Dec 1999.</span>

</li>

<li id="cite_note-SForge-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-SForge_14-0">^</a></b></span> <span class="reference-text"> <a rel="nofollow" class="external autonumber" href="http://sourceforge.net/blog/january-2014-potm/ SourceForge">[3]</a> Minsky - Project of the month January 2014. Interview with Minsky development team. Accessed January 2014</span>

</li>

<li id="cite_note-Tay_Feedback-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-Tay_Feedback_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Tay_Feedback_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Michael J. Radzicki and Robert A. Taylor (2008). <a rel="nofollow" class="external text" href="http://www.systemdynamics.org/DL-IntroSysDyn/start.htm">"Feedback"</a>. In: <i>U.S. Department of Energy's Introduction to System Dynamics</i>. Retrieved 23 October 2008.</span>

</li>

</ol></div></div>

<div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div>

<ul><li><cite id="CITEREFKypuros2013" class="citation book cs1">Kypuros, Javier (2013). <i>System dynamics and control with bond graph modeling</i>. Boca Raton: Taylor & Francis. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1466560758</bdi>.</cite></li>

<li><cite id="CITEREFForrester1961" class="citation book cs1">Forrester, Jay W. (1961). <a rel="nofollow" class="external text" href="https://archive.org/details/industrialdynami0000forr/"><i>Industrial Dynamics</i></a>. M.I.T. Press.</cite></li>

<li><cite id="CITEREFForrester1969" class="citation book cs1">Forrester, Jay W. (1969). <i>Urban Dynamics</i>. Pegasus Communications. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-1-883823-39-9</bdi>.</cite></li>

<li><cite id="CITEREFMeadows1972" class="citation book cs1">Meadows, Donella H. (1972). <a href="Limits_to_Growth" class="mw-redirect" title="Limits to Growth"><i>Limits to Growth</i></a>. New York: University books. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-87663-165-2</bdi>.</cite></li>

<li><cite id="CITEREFMorecroft2007" class="citation book cs1">Morecroft, John (2007). <i>Strategic Modelling and Business Dynamics: A Feedback Systems Approach</i>. John Wiley & Sons. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-470-01286-4</bdi>.</cite></li>

<li><cite id="CITEREFRoberts1978" class="citation book cs1">Roberts, Edward B. (1978). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/managerialapplic0000unse"><i>Managerial Applications of System Dynamics</i></a></span>. Cambridge: MIT Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-262-18088-7</bdi>.</cite></li>

<li><cite id="CITEREFRanders1980" class="citation book cs1">Randers, Jorgen (1980). <i>Elements of the System Dynamics Method</i>. Cambridge: MIT Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-915299-39-3</bdi>.</cite></li>

<li><cite id="CITEREFSenge1990" class="citation book cs1">Senge, Peter (1990). <a href="The_Fifth_Discipline" title="The Fifth Discipline"><i>The Fifth Discipline</i></a>. Currency. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-385-26095-4</bdi>.</cite></li>

<li><cite id="CITEREFSterman2000" class="citation book cs1">Sterman, John D. (2000). <a href="Business_dynamics" class="mw-redirect" title="Business dynamics"><i>Business Dynamics: Systems thinking and modeling for a complex world</i></a>. McGraw Hill. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-0-07-231135-8</bdi>.</cite></li></ul>

<div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .infobox .side-box{font-size:100%}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1237033735">

/* start https://en.wikipedia.org/ */

@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}

/* end https://en.wikipedia.org/ */

</style><div class="side-box side-box-right sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">

/* start https://en.wikipedia.org/ */

.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}

/* end https://en.wikipedia.org/ */

</style>

<div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Systems_dynamics" class="extiw external" title="commons:Category:Systems dynamics">systems dynamics</a></span>.</div></div>

</div>

<ul><li><a rel="nofollow" class="external text" href="http://www.systemdynamics.org/">System Dynamics Society</a></li>

<li><a rel="nofollow" class="external text" href="http://www.systemdynamics.org/DL-IntroSysDyn/">Study Prepared for the U.S. Department of Energy's Introducing System Dynamics - </a></li>

<li><a rel="nofollow" class="external text" href="http://web.mit.edu/jsterman/www/DID.html">Desert Island Dynamics</a> "An Annotated Survey of the Essential System Dynamics Literature"</li>

<li><a rel="nofollow" class="external text" href="https://true-world.com/htm/en/index.html">True World : Temporal Reasoning Universal Elaboration</a> : System Dynamics software used for diagrams in this article (free)</li></ul>

/* start https://en.wikipedia.org/ */

.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}

/* end https://en.wikipedia.org/ */

</style><style data-mw-deduplicate="TemplateStyles:r1236075235">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox" aria-labelledby="Systems_science494" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><style data-mw-deduplicate="TemplateStyles:r1239400231">

/* start https://en.wikipedia.org/ */

.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}

/* end https://en.wikipedia.org/ */

</style><div id="Systems_science494" style="font-size:114%;margin:0 4em"><a href="Systems_science" title="Systems science">Systems science</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="System" title="System">System</a><br>types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Biological_system" title="Biological system">Biological</a></li>

<li><a href="Complex_system" title="Complex system">Complex</a></li>

<li><a href="Coupled_human%E2%80%93environment_system" title="Coupled human–environment system">Coupled human–environment</a></li>

<li><a href="Ecosystem" title="Ecosystem">Ecological</a></li>

<li><a href="Economic_system" title="Economic system">Economic</a></li>

<li><a href="Information_system" title="Information system">Information</a></li>

<li><a href="Multi-agent_system" title="Multi-agent system">Multi-agent</a></li>

<li><a href="Nervous_system" title="Nervous system">Nervous</a></li>

<li><a href="Recommender_system" title="Recommender system">Recommender</a></li>

<li><a href="Social_system" title="Social system">Social</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Doubling_time" title="Doubling time">Doubling time</a></li>

<li><a href="Twelve_leverage_points" title="Twelve leverage points">Leverage points</a></li>

<li><a href="Limiting_factor" title="Limiting factor">Limiting factor</a></li>

<li><a href="Negative_feedback" title="Negative feedback">Negative feedback</a></li>

<li><a href="Positive_feedback" title="Positive feedback">Positive feedback</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theoretical<br>fields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Control_theory" title="Control theory">Control theory</a></li>

<li><a href="Cybernetics" title="Cybernetics">Cybernetics</a></li>

<li><a href="Earth_system_science" title="Earth system science">Earth system science</a></li>

<li><a href="Living_systems" title="Living systems">Living systems</a></li>

<li><a href="Sociotechnical_system" title="Sociotechnical system">Sociotechnical system</a></li>

<li><a href="Systemics" title="Systemics">Systemics</a></li>

<li><a href="Urban_metabolism" title="Urban metabolism">Urban metabolism</a></li>

<li><a href="World-systems_theory" title="World-systems theory">World-systems theory</a></li></ul>

</div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Systems_analysis" title="Systems analysis">Analysis</a></li>

<li><a href="Systems_biology" title="Systems biology">Biology</a></li>

<li><a href="Systems_ecology" title="Systems ecology">Ecology</a></li>

<li><a href="Systems_engineering" title="Systems engineering">Engineering</a></li>

<li><a href="Systems_neuroscience" title="Systems neuroscience">Neuroscience</a></li>

<li><a href="Systems_pharmacology" title="Systems pharmacology">Pharmacology</a></li>

<li><a href="Systems_philosophy" title="Systems philosophy">Philosophy</a></li>

<li><a href="Systems_psychology" title="Systems psychology">Psychology</a></li>

<li><a href="Systems_theory" title="Systems theory">Theory</a> (<a href="Systems_thinking" title="Systems thinking">Systems thinking</a>)</li></ul>

</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="List_of_systems_scientists" title="List of systems scientists">Scientists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Russell_L._Ackoff" title="Russell L. Ackoff">Russell L. Ackoff</a></li>

<li><a href="Victor_Aladjev" title="Victor Aladjev">Victor Aladjev</a></li>

<li><a href="William_Ross_Ashby" class="mw-redirect" title="William Ross Ashby">William Ross Ashby</a></li>

<li><a href="Ruzena_Bajcsy" title="Ruzena Bajcsy">Ruzena Bajcsy</a></li>

<li><a href="B%C3%A9la_H._B%C3%A1n%C3%A1thy" title="Béla H. Bánáthy">Béla H. Bánáthy</a></li>

<li><a href="Gregory_Bateson" title="Gregory Bateson">Gregory Bateson</a></li>

<li><a href="Anthony_Stafford_Beer" class="mw-redirect" title="Anthony Stafford Beer">Anthony Stafford Beer</a></li>

<li><a href="Richard_E._Bellman" title="Richard E. Bellman">Richard E. Bellman</a></li>

<li><a href="Ludwig_von_Bertalanffy" title="Ludwig von Bertalanffy">Ludwig von Bertalanffy</a></li>

<li><a href="Margaret_Boden" title="Margaret Boden">Margaret Boden</a></li>

<li><a href="Alexander_Bogdanov" title="Alexander Bogdanov">Alexander Bogdanov</a></li>

<li><a href="Kenneth_E._Boulding" title="Kenneth E. Boulding">Kenneth E. Boulding</a></li>

<li><a href="Murray_Bowen" title="Murray Bowen">Murray Bowen</a></li>

<li><a href="Kathleen_Carley" title="Kathleen Carley">Kathleen Carley</a></li>

<li><a href="Mary_Cartwright" title="Mary Cartwright">Mary Cartwright</a></li>

<li><a href="C._West_Churchman" title="C. West Churchman">C. West Churchman</a></li>

<li><a href="Manfred_Clynes" title="Manfred Clynes">Manfred Clynes</a></li>

<li><a href="George_Dantzig" title="George Dantzig">George Dantzig</a></li>

<li><a href="Edsger_W._Dijkstra" title="Edsger W. Dijkstra">Edsger W. Dijkstra</a></li>

<li><a href="Fred_Emery" title="Fred Emery">Fred Emery</a></li>

<li><a href="Heinz_von_Foerster" title="Heinz von Foerster">Heinz von Foerster</a></li>

<li><a href="Stephanie_Forrest" title="Stephanie Forrest">Stephanie Forrest</a></li>

<li><a href="Jay_Wright_Forrester" title="Jay Wright Forrester">Jay Wright Forrester</a></li>

<li><a href="Barbara_J._Grosz" title="Barbara J. Grosz">Barbara Grosz</a></li>

<li><a href="Charles_A._S._Hall" title="Charles A. S. Hall">Charles A. S. Hall</a></li>

<li><a href="Mike_Jackson_(systems_scientist)" title="Mike Jackson (systems scientist)">Mike Jackson</a></li>

<li><a href="Lydia_Kavraki" title="Lydia Kavraki">Lydia Kavraki</a></li>

<li><a href="James_J._Kay" title="James J. Kay">James J. Kay</a></li>

<li><a href="Faina_Mihajlovna_Kirillova" class="mw-redirect" title="Faina Mihajlovna Kirillova">Faina M. Kirillova</a></li>

<li><a href="George_Klir" title="George Klir">George Klir</a></li>

<li><a href="Allenna_Leonard" title="Allenna Leonard">Allenna Leonard</a></li>

<li><a href="Edward_Norton_Lorenz" title="Edward Norton Lorenz">Edward Norton Lorenz</a></li>

<li><a href="Niklas_Luhmann" title="Niklas Luhmann">Niklas Luhmann</a></li>

<li><a href="Humberto_Maturana" title="Humberto Maturana">Humberto Maturana</a></li>

<li><a href="Margaret_Mead" title="Margaret Mead">Margaret Mead</a></li>

<li><a href="Donella_Meadows" title="Donella Meadows">Donella Meadows</a></li>

<li><a href="Mihajlo_D._Mesarovic" title="Mihajlo D. Mesarovic">Mihajlo D. Mesarovic</a></li>

<li><a href="James_Grier_Miller" title="James Grier Miller">James Grier Miller</a></li>

<li><a href="Radhika_Nagpal" title="Radhika Nagpal">Radhika Nagpal</a></li>

<li><a href="Howard_T._Odum" title="Howard T. Odum">Howard T. Odum</a></li>

<li><a href="Talcott_Parsons" title="Talcott Parsons">Talcott Parsons</a></li>

<li><a href="Ilya_Prigogine" title="Ilya Prigogine">Ilya Prigogine</a></li>

<li><a href="Qian_Xuesen" title="Qian Xuesen">Qian Xuesen</a></li>

<li><a href="Anatol_Rapoport" title="Anatol Rapoport">Anatol Rapoport</a></li>

<li><a href="John_Seddon" title="John Seddon">John Seddon</a></li>

<li><a href="Peter_Senge" title="Peter Senge">Peter Senge</a></li>

<li><a href="Claude_Shannon" title="Claude Shannon">Claude Shannon</a></li>

<li><a href="Katia_Sycara" title="Katia Sycara">Katia Sycara</a></li>

<li><a href="Eric_Trist" title="Eric Trist">Eric Trist</a></li>

<li><a href="Francisco_Varela" title="Francisco Varela">Francisco Varela</a></li>

<li><a href="Manuela_M._Veloso" title="Manuela M. Veloso">Manuela M. Veloso</a></li>

<li><a href="Kevin_Warwick" title="Kevin Warwick">Kevin Warwick</a></li>

<li><a href="Norbert_Wiener" title="Norbert Wiener">Norbert Wiener</a></li>

<li><a href="Jennifer_Wilby" title="Jennifer Wilby">Jennifer Wilby</a></li>

<li><a href="Anthony_Wilden" title="Anthony Wilden">Anthony Wilden</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Systems_theory_in_anthropology" title="Systems theory in anthropology">Systems theory in anthropology</a></li>

<li><a href="Systems_theory_in_archaeology" title="Systems theory in archaeology">Systems theory in archaeology</a></li>

<li><a href="Systems_theory_in_political_science" title="Systems theory in political science">Systems theory in political science</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Organizations</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<li><a href="Principia_Cybernetica" title="Principia Cybernetica">Principia Cybernetica</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> <b>Category</b></li>

<li><span class="noviewer" typeof="mw:File"></span> <b><a href="Portal%3ASystems_science" title="Portal:Systems science">Portal</a></b></li>

<li><span class="noviewer" typeof="mw:File"><span title="Commons page"></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Systems_theory" class="extiw external" title="commons:Category:Systems theory">Commons</a></b></li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Systems_engineering118" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Systems_engineering118" style="font-size:114%;margin:0 4em"><a href="Systems_engineering" title="Systems engineering">Systems engineering</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Subfields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Aerospace_engineering" title="Aerospace engineering">Aerospace engineering</a></li>

<li><a href="Biological_systems_engineering" title="Biological systems engineering">Biological systems engineering</a></li>

<li><a href="Cognitive_systems_engineering" title="Cognitive systems engineering">Cognitive systems engineering</a></li>

<li><a href="Configuration_management" title="Configuration management">Configuration management</a></li>

<li><a href="Earth_systems_engineering_and_management" title="Earth systems engineering and management">Earth systems engineering and management</a></li>

<li><a href="Electrical_engineering" title="Electrical engineering">Electrical engineering</a></li>

<li><a href="Enterprise_systems_engineering" title="Enterprise systems engineering">Enterprise systems engineering</a></li>

<li><a href="Health_systems_engineering" title="Health systems engineering">Health systems engineering</a></li>

<li><a href="Performance_engineering" title="Performance engineering">Performance engineering</a></li>

<li><a href="Reliability_engineering" title="Reliability engineering">Reliability engineering</a></li>

<li><a href="Safety_engineering" title="Safety engineering">Safety engineering</a></li>

<li><a href="Stanford_torus" title="Stanford torus">Sociocultural Systems Engineering</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Processes</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Requirements_engineering" title="Requirements engineering">Requirements engineering</a></li>

<li><a href="Functional_Analysis_and_Allocation" class="mw-redirect" title="Functional Analysis and Allocation">Functional Analysis and Allocation</a></li>

<li><a href="System_integration" title="System integration">System integration</a></li>

<li><a href="Verification_and_validation" title="Verification and validation">Verification and validation</a></li>

<li><a href="Design_review" title="Design review">Design review</a></li>

<li><a href="System_of_systems_engineering" title="System of systems engineering">System of systems engineering</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Business_process" title="Business process">Business process</a></li>

<li><a href="Fault_tolerance" title="Fault tolerance">Fault tolerance</a></li>

<li><a href="System" title="System">System</a></li>

<li><a href="System_lifecycle" class="mw-redirect" title="System lifecycle">System lifecycle</a></li>

<li><a href="V-model" title="V-model">V-Model</a></li>

<li><a href="Systems_development_life_cycle" title="Systems development life cycle">Systems development life cycle</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Tools</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Decision-making" title="Decision-making">Decision-making</a></li>

<li><a href="Function_model" title="Function model">Function modelling</a></li>

<li><a href="Mathematical_optimization" title="Mathematical optimization">Optimization</a></li>

<li><a href="Quality_function_deployment" title="Quality function deployment">Quality function deployment</a></li>

<li><a href="Spare_part" title="Spare part">Spare part</a></li>

<li><a href="Systems_Modeling_Language" class="mw-redirect" title="Systems Modeling Language">Systems Modeling Language</a></li>

<li><a href="Systems_analysis" title="Systems analysis">Systems analysis</a></li>

<li><a href="Systems_modeling" title="Systems modeling">Systems modeling</a></li>

<li><a href="Work_breakdown_structure" title="Work breakdown structure">Work breakdown structure</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="James_S._Albus" title="James S. Albus">James S. Albus</a></li>

<li><a href="Ruzena_Bajcsy" title="Ruzena Bajcsy">Ruzena Bajcsy</a></li>

<li><a href="Benjamin_S._Blanchard" title="Benjamin S. Blanchard">Benjamin S. Blanchard</a></li>

<li><a href="Wernher_von_Braun" title="Wernher von Braun">Wernher von Braun</a></li>

<li><a href="Kathleen_Carley" title="Kathleen Carley">Kathleen Carley</a></li>

<li><a href="Harold_Chestnut" title="Harold Chestnut">Harold Chestnut</a></li>

<li><a href="Wolt_Fabrycky" title="Wolt Fabrycky">Wolt Fabrycky</a></li>

<li><a href="Barbara_Grosz" class="mw-redirect" title="Barbara Grosz">Barbara Grosz</a></li>

<li><a href="Arthur_David_Hall_III" title="Arthur David Hall III">Arthur David Hall III</a></li>

<li><a href="Derek_Hitchins" title="Derek Hitchins">Derek Hitchins</a></li>

<li><a href="Robert_E._Machol" title="Robert E. Machol">Robert E. Machol</a></li>

<li><a href="Radhika_Nagpal" title="Radhika Nagpal">Radhika Nagpal</a></li>

<li><a href="Simon_Ramo" title="Simon Ramo">Simon Ramo</a></li>

<li><a href="Joseph_Francis_Shea" title="Joseph Francis Shea">Joseph Francis Shea</a></li>

<li><a href="Katia_Sycara" title="Katia Sycara">Katia Sycara</a></li>

<li><a href="Manuela_M._Veloso" title="Manuela M. Veloso">Manuela M. Veloso</a></li>

<li><a href="John_N._Warfield" title="John N. Warfield">John N. Warfield</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related fields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Control_engineering" title="Control engineering">Control engineering</a></li>

<li><a href="Computer_engineering" title="Computer engineering">Computer engineering</a></li>

<li><a href="Industrial_engineering" title="Industrial engineering">Industrial engineering</a></li>

<li><a href="Operations_research" title="Operations research">Operations research</a></li>

<li><a href="Project_management" title="Project management">Project management</a></li>

<li><a href="Quality_management" title="Quality management">Quality management</a></li>

<li><a href="Risk_management" title="Risk management">Risk management</a></li>

<li><a href="Software_engineering" title="Software engineering">Software engineering</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li>Category</li></ul>

</div></td></tr></tbody></table></div>

<div class="navbox-styles"></div><div role="navigation" class="navbox" aria-labelledby="Energy_modeling343" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Energy_modeling343" style="font-size:114%;margin:0 4em"><a href="Energy_modeling" title="Energy modeling">Energy modeling</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Models</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="MARKAL" title="MARKAL">MARKAL</a></li>

<li><a href="Prospective_Outlook_on_Long-term_Energy_Systems" title="Prospective Outlook on Long-term Energy Systems">POLES</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Open data</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="OpenEI" title="OpenEI">OpenEI</a></li>

<li><a href="Reegle" title="Reegle">Reegle</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Open_energy_system_databases" title="Open energy system databases">Open energy system databases</a></li>

<li><a href="Open_energy_system_models" title="Open energy system models">Open energy system models</a></li></ul>

<ul><li><a href="Climate_change_mitigation_scenarios" class="mw-redirect" title="Climate change mitigation scenarios">Climate change mitigation scenarios</a></li>

<li><a href="Computer_simulation" title="Computer simulation">Computer simulation</a></li>

<li><a href="Energy_modeling" title="Energy modeling">Energy modeling</a></li>

<li><a href="Mathematical_optimization" title="Mathematical optimization">Mathematical optimization</a></li>

<li><a href="Scenario_analysis" class="mw-redirect" title="Scenario analysis">Scenario analysis</a></li>

</ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Applications</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Electricity_market" title="Electricity market">Electricity market</a></li>

<li><a href="Electric_power_transmission" title="Electric power transmission">Electric power transmission</a></li>

<li><a href="Energy_market" title="Energy market">Energy market</a></li>

<li><a href="Energy_planning" title="Energy planning">Energy planning</a></li>

<li><a href="Energy_policy" title="Energy policy">Energy policy</a></li>

<li><a href="Integrated_assessment_modelling" title="Integrated assessment modelling">Integrated assessment modelling</a></li></ul>

</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Hartmut_Bossel" title="Hartmut Bossel">Hartmut Bossel</a></li>

<li><a href="Joseph_DeCarolis" title="Joseph DeCarolis">Joe DeCarolis</a></li>

<li><a href="Mark_Z._Jacobson" title="Mark Z. Jacobson">Mark Jacobson</a></li>

<li><a href="John_A._Laitner" title="John A. Laitner">John Laitner</a></li>

<li><a href="John_Weyant" title="John Weyant">John Weyant</a></li></ul>

<ul><li><a href="Energy_Modeling_Forum" title="Energy Modeling Forum">Energy Modeling Forum</a></li>

<li><a href="Open_Energy_Modelling_Initiative" title="Open Energy Modelling Initiative">openmod initiative</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div>

<ul><li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Economics models</li>

<li><span class="noviewer" typeof="mw:File"><span title="Category"></span></span> Energy models</li></ul>

</div></td></tr></tbody></table></div>

/* start https://en.wikipedia.org/ */

.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}

/* end https://en.wikipedia.org/ */

</style></div><div role="navigation" class="navbox authority-control" aria-label="Navbox674" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Authority control databases: National </th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4058802-6">Germany</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="systémová dynamika"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph846528&CON_LNG=ENG">Czech Republic</a></span></span></li></ul></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2025-06-06" href="https://en.wikipedia.org/wiki/?title=System_dynamics&oldid=1294252720">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

</div>

</div></div>

</div>

</main>

</div>

</body></html>