A qualitative physics based on confluences
Artificial Intelligence - Special volume on qualitative reasoning about physical systems
Artificial Intelligence - Special volume on qualitative reasoning about physical systems
Artificial Intelligence
Qualitative reasoning: modeling and simulation with incomplete knowledge
Qualitative reasoning: modeling and simulation with incomplete knowledge
The Mathematica Book
A qualitative method to construct phase portraits
AAAI'93 Proceedings of the eleventh national conference on Artificial intelligence
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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.