Qualitative reasoning and bifurcations in dynamic systems

Abstract

A bifurcation occurs in a dynamic system when the structure of the system itself and therefore also its qualitative behavior change as a result of changes in one of the system's parameters. In most cases, an infinitesimal change in one of the parameters make the dynamic system exhibit dramatic changes. In this paper, we present a framework (QRBD) for performing qualitative analysis of dynamic systems exhibiting bifurcations. QRBD performs a simulation of the system with bifurcations, in the presence of perturbations, producing accounts for all events in the system, given a qualitative description of the changes it undergoes. In such a sequence of events, we include catastrophic changes due to perturbations and bifurcations, and hysteresis. QRBD currently works with first-order systems with only one varying parameter. We propose the qualitative representations and algorithm that enable us to reason about the changes a dynamic system undergoes when exhibiting bifurcations, in the presence of perturbations. © Springer-Verlag Berlin Heidelberg 2006.