The concept of energy in the analysis of system dynamics models

Abstract

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 workenergy 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.

Refining the causal loop diagram: A tutorial for maximizing the contribution of domain expertise in computational system dynamics modeling.

“…For the example above, this would mean that even if David had a bad night’s sleep (A = 0), he could make up for its effect on his concentration by having breakfast (B > 0). For more information on common types of interactions we refer the reader to (Hayward et al, 2014).…”

A comparison of loop dominance methods: measures and meaning

“…Once disturbed, the system changes under its own momentum, with B 1 a diffusion force, resisting the behaviour until equilibrium is reached. The interpretative framework was further extended to consider energy, that is, the cumulative effect of these forces, measured by loop impact, over time (Hayward and Roach, 2022). Energy in each stock-flow subsystem is conserved, provided account is taken of the kinetic energy of the stocks, a measure of how quickly the stocks change.…”

“…where, for t > t c stock per unit time by a loop is called the loop's power. Power is the loop impact multiplied by the net flow squared (Hayward and Roach, 2022). Thus, using (A.7-A.11) the power of the loops in the Workforce-Inventory system are:…”

“…The cumulative measure Work Done that describes the energy flows, and the related Loop Power, were computed numerically using the methods of Hayward and Roach (2022) and checked where possible using the analytical computations in this article.…”

“…The second category is Eigenvalue Elasticity Analysis (EEA) (Oliva, 2020). We will further divide the pathway methods into instantaneous measures, where a loop's influence is measured at each point in time, and cumulative measures, where the influence is determined over a time interval (Hayward and Roach, 2022). i We will use the Workforce-Inventory model as our case study, which has been analysed previously using the abovementioned methods.…”