# System dynamics

System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system.[1] What makes using system dynamics different from other approaches to studying complex systems is the use of feedback loops and stocks and flows. These elements help describe how even seemingly simple systems display baffling nonlinearity.

## Overview

Systems 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.

## History

System Dynamics was founded in the late 1950s by Jay W. Forrester of the MIT Sloan School of Management with the establishment of the MIT System Dynamics Group. At that time, he began applying what he had learned about systems during his work in electrical engineering to everyday kinds of systems.

Determining the exact date of the founding of the field of system dynamics is difficult and involves a certain degree of arbitrariness. Jay W. Forrester joined the faculty of the Sloan School at MIT in 1956, where he then developed what is now System Dynamics. The first published article by Jay W. Forrester in the Harvard Business Review on "Industrial Dynamics", was published in 1958.

The members of System Dynamics Society have chosen 1957 to mark the occasion as it is the year in which the work leading to that article, which described the dynamics of a manufacturing supply chain, was done.

## Topics in systems dynamics

The 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 diagrams

A 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 diagrams

The 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.

File:Simple stock and flow diagram.gif
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

### Equations

The 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:

• Define the problem boundary
• Identify the most important stocks and flows that change these stock levels
• Identify sources of information that impact the flows
• Identify the main feedback loops
• Draw a causal loop diagram that links the stocks, flows and sources of information
• Write the equations that determine the flows
• Estimate the parameters and initial conditions. These can be estimated using statistical methods, expert opinion, market research data or other relevant sources of information.[2]
• Simulate the model and analyse results

The equations for the causal loop example are:

${\displaystyle \ Adopters=\int _{0}^{t}{\mbox{New adopters }}\,dt}$

${\displaystyle \ {\mbox{Potential adopters}}=\int _{0}^{t}{\mbox{-New adopters }}\,dt}$

${\displaystyle \ {\mbox{New adopters}}={\mbox{Innovators}}+{\mbox{Imitators}}}$

${\displaystyle \ {\mbox{Innovators}}=p\cdot {\mbox{Potential adopters}}}$

${\displaystyle \ {\mbox{Imitators}}=q\cdot {\mbox{Adopters}}\cdot {\mbox{Probability that contact has not yet adopted}}}$

${\displaystyle \ {\mbox{Probability that contact has not yet adopted}}={\frac {\mbox{Potential adopters}}{{\mbox{Potential adopters }}+{\mbox{ Adopters}}}}}$

${\displaystyle \ p=0.03}$

${\displaystyle \ q=0.4}$


### Simulation results

The 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

## Application

System 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:

• Teach system thinking reflexes to persons being coached
• Analyze and compare assumptions and mental models about the way things work
• Gain qualitative insight into the workings of a system or the consequences of a decision
• Recognize archetypes of dysfunctional systems in everyday practice

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].