System dynamics is a modelling methodology whose power lies in understanding complex situations through cause and effect. Invented in the mid-1950s by JW Forrester at MIT, it has seen much success in modelling the environment, business dynamics and social situations. Its key distinguishing feature is the use of feedback, through causal loops, as the primary driver of behaviour in social systems.

A system dynamics model is built by making dynamic hypotheses that are intended to explain observed behaviour. Their consequences can be explored using a range of methods, including mathematics and computer simulation. Even when it is not possible to predict future changes accurately, due to factors that are hard to measure or impossible to predict, it is still possible to establish principles that govern the way change occurs in given situations. It is, therefore, an ideal method for studying church growth, given the proviso that God “continues to act the same way.” He can sovereignly change situations (represented by the parameters of the model) at any time in ways that no model can predict.

The methodology is also straightforward for non-mathematicians to follow. Thus, it is ideal for presenting to a variety of audiences, such as church leaders, and involve them in the modelling process.


  • Forrester J.W. (1961). Industrial Dynamics. Pegasus Communications: Waltham: MA.
    The first book on system dynamics.
  • Forrester J.W. (1968). Principles of Systems. Pegasus Communications: Waltham: MA.
  • Meadows D. H. (1991). The Global Citizen. Washington DC: Island Press.
  • Meadows D. H., Meadows D.L. and Randers J. (1992). Beyond the Limits: Confronting Global Collapse, Envisioning A Sustainable Future. Post Mills VT: Chelsea Green.
  • Meadows D.H. & Wright D. (2009), Thinking in Systems: A Primer, Routledge.
  • Morecroft J. (2007). Strategic Modelling and Business Dynamics: A Feedback Systems Approach. John Wiley and Sons.
  • Richmond B. (2004). An Introduction to Systems Thinking with STELLA. ISEE Systems Inc.
  • Senge P.M. (1990). The Fifth Discipline: The Art and Practice of the Learning Organization, Random House Business Books.
  • Sterman J.D. (2000). Business Dynamics: Systems Thinking and Modeling for a Complex World, McGraw Hill.
    A comprehensive account of system dynamics.
  • Wolstenholme P.M. (1990). System Enquiry: A Systems Dynamics Approach, John Wiley and Sons.

Social Modelling

Approaches to modelling social systems and soft variables that are difficult to quantify.

  • Coyle G. (2000). Qualitative and quantitative modelling in system dynamics: some research questions. System Dynamics Review, 16(3), 225-244.
  • Hayward J., Jeffs R.A., Howells L. & Evans K.S. (2014). Model Building with Soft Variables: A Case Study on Riots. Proceedings of the 32nd International Conference of the System Dynamics Society, Delft, Netherlands, July 2014.
  • Jacobsen C. & Bronson R. (1987). Defining sociological concepts as variables for system dynamics modeling. System Dynamics Review, 3 (1), 1-7.
  • Levine, R. L. (1983). The paradigms of psychology and system dynamics. Proceedings of the 1st International System Dynamics Society, Chestnut Hill, Albany, NY.
  • Levine R.L. (2000). System dynamics applied to psychological and social problems. Proceedings of the 18th International Conference of the System Dynamics Society, Bergen, Norway.
  • McLucas A.C. (2003). Incorporating soft variables Into system dynamics models: A suggested method and basis for ongoing research. Proceedings of the 21st International Conference of the System Dynamics Society.
  • Nuthmann, C. (1994). Using human judgment in system dynamics models of social systems. System Dynamics Review, 10(1), 1-27.

Model Analysis

  • Ford D.N. (1999). A behavioural approach to feedback loop dominance analysis. System Dynamics Review 15(1): 3-36.
  • Duggan J, Oliva R. (2013). Methods for identifying structural dominance. System Dynamics Review, Special Virtual Issue.
  • Goncalves P. (2009). Behavior modes, pathways and overall trajectories: eigenvector and eigenvalue analysis of dynamic systems. System Dynamics Review 25(1): 35-62.
  • Hayward J. & Boswell G.P. (2014). Model Behaviour and the Concept of Loop Impact: A Practical Method. System Dynamics Review, 30(1), 29-57. DOI: 10.1002/sdr.1511
  • Hayward J. & Roach P.A. (2017). Newton’s Laws as an Interpretive Framework in System Dynamics. System Dynamics Review, 33(3-4), 183-218. DOI: 10.1002/sdr.1586.
  • Hayward J. & Roach P.A.. (2019). The concept of force in population dynamics, Physica A: Statistical Mechanics and its Applications, 531, 121736, DOI: 10.1016/j.physa.2019.121736.
  • Kampmann C.E. (2012). Feedback loop gains and system behaviour (1996). System Dynamics Review 28(4): 370-395.
  • Kampmann C.E. & Oliva R. (2009). Analytical methods for structural dominance analysis
    in system dynamics. In Encyclopedia of Complexity and Systems Science, Meyers RA (ed.), Springer: New York; 8948-8967.
  • Mojtahedzadeh M. (2011). Consistency in explaining model behaviour based on its feedback structure. System Dynamics Review 27(4): 358-373.
  • Mojtahedzadeh M., Anderson D., Richardson G.P. (2004). Using Digest to implement the pathway participation method for detecting influential system structure. System Dynamics Review 20(1): 1-20.
  • Richardson G.P. (1986). Problems with causal loop diagrams. System Dynamics Review 2(2): 158-170.
  • Richardson G.P. (1995). Loop polarity, loop dominance, and the concept of dominant polarity. System Dynamics Review 11(1): 67-88.
  • Richardson G.P. (1997). Problems in Causal Loop Diagrams Revisited, Systems Dynamics Review, 13(3), 247-252.
  • Schoenberg, W., Davidsen, P., & Eberlein, R. (2020). Understanding model behavior using the Loops that Matter method. System Dynamics Review. In press.

Modelling Techniques

  • Eberlein R.L. & Thompson J.P. (2013). Precise modeling of aging populations. System Dynamics Review, 29(2), 87-101.
  • Fiddaman, T., & Yeager, L. (2017). Dynamic cohorts: a new approach to managing detail. Presented at International System Dynamics Conference, Cambridge, MA.
  • Lamberson, P. J. (2018). Approximating individual interactions in compartmental system dynamics models. System Dynamics Review, 34(1-2), 284-326.

General Modelling

  • Richardson G.P. (2011). Reflections on the foundations of system dynamics. System Dynamics Review 27(3): 219–243.
  • Sterman, J.D. (2002). All models are wrong: reflections on becoming a systems scientist. System Dynamics Review, 18(4), 501-531.

Diffusion Modelling

  • Lyneis J.M, & Lyneis D.A. (2007). Two Loops, three loops, or four loops: pedagogic issues in explaining basic epidemic dynamics. In Proceedings of the 25th International Conference of the System Dynamics Society, System Dynamics Society: Boston, MA.



  • ISEE Systems Stella simulation software. Most church growth modelling uses this software.
  • Powersim simulation software
  • Ventana Systems for Vensim simulation software.
  • AnyLogic simulation software. Also has agent-based modelling.
  • Berkeley Madonna simulation software. Although primarily a differential equation solver there is an SD interface and it can read in Stella models.
  • NetLogo simulation software. Although mainly agent-based modelling there is an SD section with the usual notation.
  • Sheetless formerly Sysdea.