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System dynamics
Systems dynamics modeling, John Sterman 2001.
OverviewSystem dynamics is an aspect of systems theory as a method for understanding 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 chaos theory and social dynamics. 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. An example is the properties of these letters which when considered together can give rise to meaning which does not exist in the letters by themselves. This further explains the integration of tools, like language, as a more parsimonious process in the human application of easiest path adaptability through interconnected systems. Topics in systems dynamicsThe elements of system dynamics diagrams are feedback, accumulation of flows into stocks and time delays. To illustrate 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 plans and production plans. Causal loop diagramsA causal loop diagram is a visual representation of the feedback loops in a system. The causal loop diagram of the new product introduction may look as follows: 
Causal loop diagram of new product adoption 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. The second feedback loop on the left is negative reinforcement (or "balancing" and hence labeled B). Clearly growth can not continue forever, because as more and more people adopt, there remain fewer and fewer potential adopters. Both feedback loops act simultaneously, but at different times they may have different strengths. Thus one would expect growing sales in the initial years, and then declining sales in the later years. Stock and flow diagramsThe next step is to create what is termed a stock and flow diagram. A stock is the term for any entity that accumulates or depletes over time. A flow is the rate of change in a stock. 
A flow changes the rate of accumulation of the stock In our 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.
Stock and flow diagram of new product adoption EquationsThe real power of system dynamics is utilised through simulation. Although it is possible to perform the modeling in a spreadsheet, there is a variety of software packages that have been optimised for this. The steps involved in a simulation are:
The equations for the causal loop example are: \ Adopters = \int_{0} ^{t} \mbox{New adopters }\,dt \ \mbox{Potential adopters} = \int_{0} ^{t} \mbox{-New adopters }\,dt \ \mbox{New adopters}=\mbox{Innovators}+\mbox{Imitators} \ \mbox{Innovators}=p \cdot \mbox{Potential adopters} \ \mbox{Imitators}=q \cdot \mbox{Adopters} \cdot \mbox{Probability that contact has not yet adopted} \ \mbox{Probability that contact has not yet adopted}=\frac{\mbox{Potential adopters}}{\mbox{Potential adopters } + \mbox{ Adopters}} \ p=0.03 \ q=0.4 Simulation resultsThe simulation results show that the behaviour of the system would be to have growth in adopters that follows a classical s-curve shape. The increase in adopters is very slow initially, then exponential growth for a period, followed ultimately by saturation. 
Simulation results of new product adoption ApplicationSystem dynamics has found application in a wide range of areas, for example population, ecological and economic systems, which usually interact strongly with each other. System dynamics have various "back of the envelope" management applications. They are a potent tool to:
Computer software is used to simulate a system dynamics model 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 systems thinking and constructs the same causal loop diagrams 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.[3] System dynamics has been used to investigate resource dependencies, and resulting problems, in product development.[4] [5]. See also
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ca:Dinŕmica de sistemes cs:Systémová dynamika de:System Dynamics es:Dinámica de sistemas fa:??????? ????? fr:Syst%C3%A8me_dynamique hu:Rendszerdinamika nl:Systeemdynamica ja:?????????? no:Systemdynamikk pt:Dinâmica de sistemas ru:????????? ???????? sk:Systémová dynamika su:Dinamika sistim zh:????? Source: Wikipedia | The above article is available under the GNU FDL. | Edit this article
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