Qualitative Reasoning and Bifurcations in Dynamic Systems
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.
KeywordsPhase Portrait Bifurcation Diagram Bifurcation Point Qualitative Description Simulation Algorithm
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- 4.Lee, W.W., Kuipers, B.J.: A qualitative method to construct phase portraits. In: Proc.11th National Conf.on Artificial Intelligence (AAAI 1993), pp. 614–619. AAAI Press/The MIT Press, Menlo Park, Cambridge, London (1993)Google Scholar
- 5.Strogatz, S.H.: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, and Engineering. Westview Press, Cambridge, MA (1994)Google Scholar
- 7.Kuipers, B.J.: Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge. MIT Press, Cambridge (1994)Google Scholar
- 8.Wolfram, S.: The Mathematica Book. Cambridge University Press, Cambridge (2003)Google Scholar