Comparison between the Deterministic and the Probabilistic Approaches for a System Undergoing Bifurcation

Abstract

With a simple illustrative example, a comparison is made between the evolution of a system as described by the deterministic differential equations of ‘systems dynamics’, and that resulting from a deeper probabilistic analysis. It is shown that, for nonlinear systems, differences can arise in the behaviour predicted by the two methods, and therefore that considerable caution should be used in the modeling of such systems.