The Concept of Energy in the Analysis of System Dynamics Models

John Hayward, Paul Roach

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This paper applies for the first time the Newtonian concept of energy to stock-flow systems and employs it to relate system behaviour to model structure. Kinetic energy and work done are defined analytically using the concepts of loop impact and force from the Newtonian Interpretative Framework and are examined numerically within system dynamics simulations. The energy analogy is used to analyse models by understanding how loops of different orders and types act as energy sources, sinks, and exchange, using the system dynamics equivalent of the work-energy theorem. It is shown that energy describes
the cumulative effects of feedback on stock behaviour, in contrast to the instantaneous description given by existing methods of loop dominance. This approach gives additional insight over that of existing dominance methods, capturing the dynamical influence of loops even when not dominant. The analogy’s explanatory power provides quantitative and informal analysis.
Original languageEnglish
Article numbersdr.1700
Pages (from-to)5-40
Number of pages36
JournalSystem Dynamics Review
Issue number1
Early online date6 Feb 2022
Publication statusPublished - 23 Mar 2022


  • Mathematical/Model Analysis
  • Causal Loop Diagrams
  • implementation
  • loop dominance
  • kinetic energy
  • work done


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