### Modelling Methodology

System dynamics is a quantitative modelling methodology for dynamical systems using stocks, flows and feedback. The former control engineer, Jay W. Forrester at MIT, pioneered system dynamics in the late 1950s and 60s.

• Stocks are the dynamic variables of the system and represent accumulations of material, items, people, etc.
• Flows are the rates of change of stocks and represent policies that adjust stock levels.
• Feedback occurs when changes in a stock level cause other changes in system variables, which in turn make changes to the original stock. Feedback can either be reinforcing or balancing.

### Stock-Flow Diagrams

System dynamics models are expressed in a diagrammatic notation for stocks and flows. In addition, there are auxiliary variables, called converters; and connectors, representing the causal links between model elements. In the figure below, the Deer Population and the Vegetation are stocks. Their numbers accumulate or deplete over time. Births and regeneration are examples of inflows, adding deer and vegetation to their respective stocks. Deaths and consumption are outflows, taking material from the stocks. The remaining variables are called converters or auxiliaries.

The single arrows are examples of connectors. These indicate a direct causal link between elements, that is one where there is no accumulation. Thus, when Vegetation increases, vegetation availability increases immediately.

Although a system dynamics model can be reduced to differential equations (or difference equations)  the methodology offers at least three advantages over classic differential equation modelling:

1. System dynamics provides an interpretational framework where variables are seen as accumulations, and rates of change viewed as policies. This framework provides an intuitive understanding of model behaviour that can be presented to a wide audience, especially to people without higher mathematical skills. This is especially useful for models relevant to business leaders, managers and policymakers who can contribute to model construction and benefit from its results.
2. A system dynamics model preserves the causal structure between model elements and thus encapsulates the model’s assumptions and hypotheses. This enables model behaviour to be examined in terms of the contribution of the different assumptions and provides a clear link between model structure and behaviour.
3. Feedback, which emerges from the model’s causal structure, becomes a key explanatory concept for model behaviour in the system dynamics interpretational framework. Feedback helps cut through model complexity and provide elegant behavioural explanations.

### System Dynamics Bibliography

• Forrester J.W. (1961). Industrial Dynamics, Pegasus Communications: Waltham: MA.
• Forrester J.W. (1968). Principles of Systems, Pegasus Communications: Waltham: MA.
• Sterman J.D. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World, McGraw Hill.
• Richmond B. (2004). An Introduction to Systems Thinking, isee Systems, Inc.
• Meadows D.H. & Wright D. (2009), Thinking in Systems: A Primer, Routledge
• Morecroft J. (2015). Strategic Modelling and Business Dynamics: A Feedback Systems Approach, John Wiley and Sons.
• Senge P.M. (2006). The Fifth Discipline. Random House Business.
• Stroh D.P. (2015). Systems Thinking for Social Change. Chelsea Green Publishing.
• Warren K. (2015). Strategy Dynamics Essentials, CreateSpace Independent Publishing Platform.

Further information at the System Dynamics Society.