Summarizing the behaviour of complex dynamic systems

Abstract

This paper outlines a general method for summarizing the behaviour of complex dynamic systems inspired by Bayesian causal analysis. The method is universally applicable and often permits to cut the backward causal loops through which the analyzed variables seem to co-determine themselves due to the nonlinearity of the equations describing complex systems.

Causal Analysis of the Emergent Behavior of a Hybrid Dynamical System

“…This model was used in project EUSAS financed by 20 nations under the Joint Investment Program Force Protection of the European Defence Agency. Interested readers can refer to a detailed exposition with a motivating example given in [5,4]. Below we provide a brief summary of the model.…”

“…In [4] we tried to answer the question whether, in a scenario with this model, indirect social influence of nearby people was more important than external events in shaping the civilian agents' behavior. The answer provided by the causal summary of the scenario indicated that external events were more important.…”

“…Following [4], we shall briefly illustrate causal partitioning on motive fear. Its continuous dynamics is driven by the equation…”

“…These factors can be evaluated numerically. As we explained in [4], this formula is the basis for our algorithm for causal partitioning of fear into causal partition vectors, where each vector component represents the quantitative contribution of one "causing" factor. The first derivative of fear f at any moment is then represented by the causal partition vector (f E , f I ), whose components sum up to f. The first component f E stands for the cumulative contribution of the external events E F , the second f I for the cumulative contribution of fear-related social influence I F .…”

“…As mentioned, we revisit the scenario from [4], in which a crowd of civilians is looting a shop, and the approaching soldier patrol is supposed to stop the looting and disperse the crowd. The scene is shown in Fig.…”