### Overview

System Dynamics is a computer-aided approach for strategy and policy design. It uses simulation modeling based on feedback systems theory and is an analytical approach that complements systems thinking. 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 was invented in the late 1950s by Jay W. Forrester, a pioneer in engineering and computer design. His seminal book *Industrial Dynamics *(Forrester 1961) is still a significant statement of philosophy and methodology in the field. Since then, System Dynamics has developed as its own field, distinct from the larger fields of operations research and management science to which it is related. 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).

System Dynamics unites social and behavioral science with the nitty-gritty details of planning and accounting, and requires the careful design and construction of original models with many interacting variables. Although System Dynamics modeling is technically demanding, the logic and results of a good System Dynamics model are neither esoteric nor hard for decision makers to understand. And although System Dynamics models are sophisticated, they are also compact enough to run instantly on a laptop computer, permitting a whole series of alternative assumptions and scenarios to be tested quickly and thoroughly in interactive strategy development sessions

### 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.

The System Dynamics approach is founded on the scientific method. The goal of a system dynamics project is sometimes to build theoretical understanding, sometimes to implement policies for improvement, and often both. To do so, system dynamics modelers seek to: include a broad model boundary that captures important feedbacks relevant to the problem to be addressed; represent important structures in the system including accumulations and state variables, delays and nonlinearities; use behavioral decision rules for the actors and agents in the system that are grounded in first-hand study; and use the widest range of empirical data to formulate the model, estimate parameters, and build confidence in the conclusions.

Although the points below are presented as a list, modeling (and any scientific activity) is iterative – a continual process of formulating hypotheses, testing against data of all types, and revision of both formal and mental models.

The approach can be summarized as:

**Beginning with a**to focus systems thinking and modeling, involving the stakeholders whose understanding and action is required to implement change.*problem***Defining problems**, in terms of graphs over time (time series), employing actual data wherever possible.*dynamically***Striving for an***endogenous, behavioral view***of the significant dynamics of a system**, a focus inward on the structures and decision rules in a system that themselves generate or exacerbate the perceived problem.**Thinking of all concepts in the real system as quantities interconnected in loops**of information feedback and circular causality, a consequence of the endogenous point of view.**Identifying the key variables**essential to address the problem and deciding on an appropriate level of aggregation for them. System dynamics models range from highly disaggregate representations such as individual items or agents to highly aggregated representations, and can be deterministic or stochastic, as needed to address the purpose of the study.**Formulating a richly explanatory behavioral model**capable of reproducing, by itself, the dynamic problem of concern, drawing on all relevant evidence, including qualitative and quantitative data. The model is usually a computer simulation model, but is occasionally left unquantified as a map capturing the important accumulations (stocks) in the system, the flows that alter them, and the causal feedback structure determining the flows.**Testing the structure and behavior of the model**against all relevant evidence to deepen understanding and to build confidence in it, including the model’s ability to replicate historical data, ensuring the model is robust under extreme conditions, exploring the sensitivity of results to uncertainty in assumptions, and diagnosing the sources of unexpected model behavior.**Designing and testing policies to address the problem of concern**, testing these against data and comparing to real-world policies that have been tried in the system or similar settings.**Documenting the model and its supporting sources**so that it is as transparent as possible and enabling others to critique, use, and extend the work.**Working with stakeholders**and others to help translate model-based insights into implementable policies, assist in implementation, assess the results, and improve both the model and policies.

While closely related to simulation research in management science and beyond, the System Dynamics approach to modeling has a few distinctive features. It is characterized by a focus on endogenous explanations for dynamic phenomena. Dynamics are explained as arising primarily endogenously within the boundary of a model from the interactions among the elements and actors in the system, rather than from exogenous inputs. Every attempt is made to represent these causal processes realistically, consistent with available empirical evidence, and robust to extreme inputs outside of the historically observed range. System dynamics researchers strive to capture the causal processes at play and the representation of these should correspond to the real-world processes in the system under study, be consistent with available empirical evidence, and be robust to extreme inputs outside of the historically observed range. These considerations require System Dynamics modelers to draw on a wide range of qualitative and quantitative data. For example, system dynamics modelers not only use traditional econometric methods to estimate model parameters using quantitative data, but also routinely augment those methods with qualitative research methods including use of archival documents, interviews, and ethnographic methods and direct observation of decision making and organizational processes. Model testing involves quantitative assessment of the ability of the model to reproduce the behavior of the system of interest, and a wide range of additional tests including structure assessment, dimensional consistency, extreme condition, behavior reproduction, surprise behavior, sensitivity analysis, and system improvement tests, among others. Furthermore, the broad model boundary and first-hand understanding of complex, multi-stakeholder systems typically requires collaborative research involving domain experts, clients (e.g. policy makers), and system dynamics modelers. Additionally, model transparency and replicability are key, policymakers and experts are engaged throughout, and graphical model representation and intuitive variable names are utilized extensively.

**Experiments conducted in the virtual world of the model inform the design and implementation of experiments in the real world. That experience then leads to changes and improvements in the virtual world, in participants’ mental models, and in actions taken in the real world, in an iterative process of continuous improvement.**

### 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. 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 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 (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.

### 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

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 feedback upon themselves, forming causal loops. Feedback loops enable the endogenous point of view and give it structure.

### Levels and Rates

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.

### Structure Drives Behavior

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 goals of the System Dynamics approach, come from this particular distance of perspective.

### How is a Useful and Reliable Model Built

System Dynamics models are custom built to be of greatest value for the particular question at hand. The modeler works closely with the client to determine what the key action and outcome variables are and at what level of detail they need to be represented. A useful model is one that considers all of the important variables but leaves out the extraneous ones. It allows testing of all the current and possible decision options, even those that may be unusual but worth considering. And it is built in close consultation with the client in steps, with the results of one step indicating what the next step should be.

Although no model can look into the future with complete accuracy, some models are more reliable and trustworthy than others. Reliable SD modeling requires science, craft, and diligence, and even small slips can compromise the results. It is crucial to seek historical time series data for as many of the model’s outcome variables as possible, and proper numerical estimates for as many of the model’s input assumptions as possible. A model must be encircled and saturated by such evidence to be considered trustworthy.

But most assumptions will have some level of uncertainty, which is why thorough sensitivity testing is important. The purpose of such testing is to determine whether changes in assumptions, within their ranges of uncertainty, can affect conclusions regarding the relative impacts of strategic decisions. The nature of dynamic systems is such that the uncertainty in most assumptions will not matter. In the cases where it does matter, one may (a) look for additional existing data to reduce the uncertainty, (b) do more detailed modeling of the parameter in question, or (c) indicate that more research needs to be done on the parameter for a more definitive answer.

### 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 the 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.