##### Introduction to System Dynamics*

Summary:

**Overview**

System dynamics is a computer-aided approach to policy analysis and design. It applies to dynamic problems arising in complex social, managerial, economic, or ecological systems — literally any dynamic systems characterized by interdependence, mutual interaction, information feedback, and circular causality.

**The System Dynamics Approach**

The approach begins with defining problems dynamically, proceeds through mapping and modeling stages, to steps for building confidence in the model and its policy implications.

**Modeling and Simulation**

Mathematically, the basic structure of a formal system dynamics computer simulation model is a system of coupled, nonlinear, first-order differential (or integral) equations. Simulation of such systems is easily accomplished by partitioning simulated time into discrete intervals of length dt and stepping the system through time one dt at a time.

**Feedback Thinking**

Conceptually, the feedback concept is at the heart of the system dynamics approach. Diagrams of loops of information feedback and circular causality are tools for conceptualizing the structure of a complex system and for communicating model-based insights.

**Loop Dominance and Nonlinearity**

The loop concept underlying feedback and circular causality by itself is not enough, however. The explanatory power and insightfulness of feedback understandings also rest on the notions of active structure and loop dominance.

**The Endogenous Point of View**

The concept of endogenous change is fundamental to the system dynamics approach. It dictates aspects of model formulation: exogenous disturbances are seen at most as triggers of system behavior; the causes are contained within the structure of the system itself.

**System Structure**

These ideas are captured in Forrester’s (1969) organizing framework for system structure:

- Closed boundary
- Feedback loops
- Levels
- Rates
- Goal
- Observed condition
- Discrepancy
- Desired action

- Feedback loops

**Levels and Rates**

Stocks (levels) and the flows (rates) that affect them are essential components of system structure. Stocks (accumulations, state variables) are the memory of a dynamic system and are the sources of its disequilibrium and dynamic behavior.

**Behavior as a Consequence of Structure**

The system dynamics approach emphasizes a continuous view. The continuous view strives to look beyond events to see the dynamic patterns underlying them. Moreover, the continuous view focuses not on discrete decisions but on the policy structure underlying decisions. Events and decisions are seen as surface phenomena that ride on an underlying tide of system structure and behavior.

***Adapted from** GP Richardson, *System Dynamics*. In *Encyclopedia of Operations Research and Management Science*, Saul Gass and Carl Harris, eds., Kluwer Academic Publishers, 1999/2011.

**Suggestions for Further Reading**

Complete article:

System dynamics is a computer-aided approach to policy analysis and design. It applies to dynamic problems arising in complex social, managerial, economic, or ecological systems — literally any dynamic systems characterized by interdependence, mutual interaction, information feedback, and circular causality.

The field developed initially from the work of Jay W. Forrester. His seminal book Industrial Dynamics (Forrester 1961) is still a significant statement of philosophy and methodology in the field. Within ten years of its publication, the span of applications grew from corporate and industrial problems to include the management of research and development, urban stagnation and decay, commodity cycles, and the dynamics of growth in a finite world. It is now applied in economics, public policy, environmental studies, defense, theory-building in social science, and other areas, as well as its home field, management. The name industrial dynamics no longer does justice to the breadth of the field, so it has become generalized to system dynamics. The modern name suggests links to other systems methodologies, but the links are weak and misleading. System dynamics emerges out of servomechanisms engineering, not general systems theory or cybernetics (Richardson 1991).

The system dynamics approach involves:

- Defining problems dynamically, in terms of graphs over time.
- Striving for an endogenous, behavioral view of the significant dynamics of a system, a focus inward on the characteristics of a system that themselves generate or exacerbate the perceived problem.
- Thinking of all concepts in the real system as continuous quantities interconnected in loops of information feedback and circular causality.
- Identifying independent stocks or accumulations (levels) in the system and their inflows and outflows (rates).
- Formulating a behavioral model capable of reproducing, by itself, the dynamic problem of concern. The model is usually a computer simulation model expressed in nonlinear equations, but is occasionally left unquantified as a diagram capturing the stock-and-flow/causal feedback structure of the system.
- Deriving understandings and applicable policy insights from the resulting model.
- Implementing changes resulting from model-based understandings and insights.

Mathematically, the basic structure of a formal system dynamics computer simulation model is a system of coupled, nonlinear, first-order differential (or integral) equations,

where x is a vector of levels (stocks or state variables), p is a set of parameters, and f is a nonlinear vector-valued function.

Simulation of such systems is easily accomplished by partitioning simulated time into discrete intervals of length dt and stepping the system through time one dt at a time. Each state variable is computed from its previous value and its net rate of change x’(t): x(t) = x(t-dt) + dt * x’(t-dt). In the earliest simulation language in the field (DYNAMO) this equation was written with time scripts K (the current moment), J (the previous moment), and JK (the interval between time J and K): X.K = X.J + DT * XRATE.JK (see, e.g., Richardson and Pugh 1981). The computation interval dt is selected small enough to have no discernible effect on the patterns of dynamic behavior exhibited by the model. In more recent simulation environments, more sophisticated integration schemes are available (although the equation written by the user may look like this simple Euler integration scheme), and time scripts may not be in evidence. Important current simulation environments include Vensim (Ventana Systems, www.vensim.com), STELLA and iThink (isee Systems, www.iseesystems.com), PowerSim (www.powersim.com), and AnyLogic North America, LLC. (AnyLogic, www.anylogic.com).

Forrester’s original work stressed a continuous approach, but increasingly modern applications of system dynamics contain a mix of discrete difference equations and continuous differential or integral equations. Some practitioners associated with the field of system dynamics work on the mathematics of such structures, including the theory and mechanics of computer simulation, analysis and simplification of dynamic systems, policy optimization, dynamical systems theory, and complex nonlinear dynamics and deterministic chaos.

The main applied work in the field, however, focuses on understanding the dynamics of complex systems for the purpose of policy analysis and design. The conceptual tools and concepts of the field — including feedback thinking, stocks and flows, the concept of feedback loop dominance, and an endogenous point of view — are as important to the field as its simulation methods.

Conceptually, the feedback concept is at the heart of the system dynamics approach. Diagrams of loops of information feedback and circular causality are tools for conceptualizing the structure of a complex system and for communicating model-based insights. Intuitively, a feedback loop exists when information resulting from some action travels through a system and eventually returns in some form to its point of origin, potentially influencing future action. If the tendency in the loop is to reinforce the initial action, the loop is called a positive or reinforcing feedback loop; if the tendency is to oppose the initial action, the loop is called a negative or balancing feedback loop. The sign of the loop is called its polarity. Balancing loops can be variously characterized as goal-seeking, equilibrating, or stabilizing processes. They can sometimes generate oscillations, as when a pendulum seeking its equilibrium goal gathers momentum and overshoots it. Reinforcing loops are sources of growth or accelerating collapse; they are disequilibrating and destabilizing. Combined, reinforcing and balancing circular causal feedback processes can generate all manner of dynamic patterns.

**Loop Dominance and Nonlinearity **

The loop concept underlying feedback and circular causality by itself is not enough, however. The explanatory power and insightfulness of feedback understandings also rest on the notions of active structure and loop dominance. Complex systems change over time. A crucial requirement for a powerful view of a dynamic system is the ability of a mental or formal model to change the strengths of influences as conditions change, that is to say, the ability to shift active or dominant structure.

In a system of equations, this ability to shift loop dominance comes about endogenously from nonlinearities in the system. For example, the S-shaped dynamic behavior of the classic logistic growth model (dP/dt = aP – bP2) can be seen as the consequence of a shift in loop dominance from a positive, self-reinforcing feedback loop (aP) producing exponential-like growth to a negative balancing feedback loop (-bP2) that brings the system to its eventual goal. Only nonlinear models can endogenously alter their active or dominant structure and shift loop dominance. From a feedback perspective, the ability of nonlinearities to generate shifts in loop dominance and capture the shifting nature of reality is the fundamental reason for advocating nonlinear models of social system behavior.

The concept of endogenous change is fundamental to the system dynamics approach. It dictates aspects of model formulation: exogenous disturbances are seen at most as triggers of system behavior (like displacing a pendulum); the causes are contained within the structure of the system itself (like the interaction of a pendulum’s position and momentum that produces oscillations). Corrective responses are also not modeled as functions of time, but are dependent on conditions within the system. Time by itself is not seen as a cause.

But more importantly, theory building and policy analysis are significantly affected by this endogenous perspective. Taking an endogenous view exposes the natural compensating tendencies in social systems that conspire to defeat many policy initiatives. Feedback and circular causality are delayed, devious, and deceptive. For understanding, system dynamics practitioners strive for an endogenous point of view. The effort is to uncover the sources of system behavior that exist within the structure of the system itself.

These ideas are captured in Forrester’s (1969) organizing framework for system structure:

- Closed boundary
- Feedback loops
- Levels
- Rates
- Goal
- Observed condition
- Discrepancy
- Desired action

- Feedback loops

The closed boundary signals the endogenous point of view. The word closed here does not refer to open and closed systems in the general system sense, but rather refers to the effort to view a system as causally closed. The modeler’s goal is to assemble a formal structure that can, by itself, without exogenous explanations, reproduce the essential characteristics of a dynamic problem.

The causally closed system boundary at the head of this organizing framework identifies the endogenous point of view as the feedback view pressed to an extreme. Feedback thinking can be seen as a consequence of the effort to capture dynamics within a closed causal boundary. Without causal loops, all variables must trace the sources of their variation ultimately outside a system. Assuming instead that the causes of all significant behavior in the system are contained within some closed causal boundary forces causal influences to feed back upon themselves, forming causal loops. Feedback loops enable the endogenous point of view and give it structure.

Stocks (levels) and the flows (rates) that affect them are essential components of system structure. A map of causal influences and feedback loops is not enough to determine the dynamic behavior of a system. A constant inflow yields a linearly rising stock; a linearly rising inflow yields a stock rising along a parabolic path, and so on. Stocks (accumulations, state variables) are the memory of a dynamic system and are the sources of its disequilibrium and dynamic behavior.

Forrester (1961) placed the operating policies of a system among its rates (flows), many of which assume the classic structure of a balancing feedback loop striving to take action to reduce the discrepancy between the observed condition of the system and a goal. The simplest such rate structure results in an equation of the form NETFLOW = (GOAL – STOCK)/(ADJTIM), where ADJTIM is the time over which the level adjusts to reach the goal.

**Behavior is a Consequence of System Structure **

The importance of levels and rates appears most clearly when one takes a continuous view of structure and dynamics. Although a discrete view, focusing on separate events and decisions, is entirely compatible with an endogenous feedback perspective, the system dynamics approach emphasizes a continuous view. The continuous view strives to look beyond events to see the dynamic patterns underlying them. Moreover, the continuous view focuses not on discrete decisions but on the policy structure underlying decisions. Events and decisions are seen as surface phenomena that ride on an underlying tide of system structure and behavior. It is that underlying tide of policy structure and continuous behavior that is the system dynamicist’s focus.

There is thus a distancing inherent in the system dynamics approach — not so close as to be confused by discrete decisions and myriad operational details, but not so far away as to miss the critical elements of policy structure and behavior. Events are deliberately blurred into dynamic behavior. Decisions are deliberately blurred into perceived policy structures. Insights into the connections between system structure and dynamic behavior, which are the goal of the system dynamics approach, come from this particular distance of perspective.

**Suggestions for Further Reading **

The System Dynamics Review, the journal of the System Dynamics Society, is the best source of current activity in the field, including methodological advances and applications. Other important journal sources include Management Science, the European Journal of Operational Research (EJOR), the Journal of the Operational Research Society (JORS), and Systems Research and Behavioral Science. For texts on the modeling process in system dynamics, see Sterman (2000), Maani and Cavana (2007), Ford (2009), Morecroft, (2007) , Wolstenholme (1990), and Richardson and Pugh (1981).

An early, interesting collection of applications is Roberts (1978); Richardson (1996) is a more recent two-volume edited collection in the same spirit, containing prize-winning work in philosophical background, dynamic decision making, applications in the private and public sectors, and techniques for modeling with management.

A current direction within the field is the use of model-based insights for organizational learning, represented most forcefully in Senge (1990) and Morecroft and Sterman (1994). The important new effort to build models with relatively large groups of experts and stakeholders, known as group model building, is described in Vennix (1996) and Richardson and Andersen (2010).

Richardson (1991/1999) puts the endogenous feedback perspective of the system dynamics approach in its historical context and includes an extensive bibliography.

**References **

Ford, A. 2009. Modeling the Environment. Washington, DC: Island Press.

Forrester, J.W. 1961. Industrial Dynamics. Cambridge, MA: The MIT Press. Reprinted by Pegasus

Communications, Waltham, MA.

Forrester, J.W. 1969. Urban Dynamics. Cambridge, MA: The MIT Press. Reprinted by Pegasus Communications,

Waltham, MA.

Maani, K. E. and R. Y. Cavana. 2007. Systems Thinking, System Dynamics: Understanding Change and Complexity.

Aukland: Printice Hall.

Morecroft, J. D. W. 2007. Strategic Modeling and Business Dynamics: a Feedback Systems Approach. Chichester:

Wiley.

Morecroft, J. D. W. and J. D. Sterman, Eds. 1994. Modeling for Learning Organizations. System Dynamics Series.

Cambridge, MA: Pegasus Communications.

Richardson, G.P. 1991/1999. Feedback Thought in Social Science and Systems Theory. Philadelphia: University of

Pennsylvania Press; reprinted by Pegasus Communications, Waltham, MA.

Richardson, G.P., Ed. 1996. Modelling for Management: Simulation in Support of Systems Thinking. International

Library of Management. Aldershot, UK: Dartmouth Publishing Company.

Richardson, G.P. and D. F. Andersen. 2010. Systems Thinking, Mapping, and Modeling for Group Decision and

Negotiation, Handbook for Group Decision and Negotiation, C Eden and DN Kilgour, eds. Dordrecht:

Springer, 2010, pp. 313-324.

Richardson, G.P. and A.L. Pugh III. 1981. Introduction to System Dynamics Modeling with DYNAMO. Cambridge,

MA: The MIT Press. Reprinted by Pegasus Communications, Waltham, MA.

Roberts, E.B. 1978, ed. Managerial Applications of System Dynamics. Cambridge, MA: The MIT Press. Reprinted

by Pegasus Communications, Waltham, MA.

Senge, P.M. The Fifth Discipline: The Art and Practice of the Learning Organization. New York:

Doubleday/Currency.

Sterman, J.D. 2000. Business Dynamics: Systems Thinking and Modeling for a Complex World. Boston: Irwin

McGraw-Hill.

System Dynamics Review. 1985-present. Chichester, U.K.: Wiley, Ltd.

Vennix, J. A. M. 1996. Group Model Building: Facilitating Team Learning Using System Dynamics. Chichester:

Wiley.

Wolstenholme, E.F. 1990. System Enquiry: a System Dynamics Approach. Chichester, U.K.: John Wiley & Sons,

Ltd.