Studies on Development of A Software System for Qualitative Analysis of Dynamical Systems

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In engineering problem solving, analysis of nonlinear differential equations plays a crucial part. This research aimed at development of a software system which can analyze the qualitative behavior of nonlinear ordinary differential equations with two unknowns, by integrating knowledge-based and numerial methods using qualitative reasoning techniques.We have achieved the following accomphshments with respect to the above research goal :1. We have devised flow patterns as a means for representing geometric features of solution curves of ordinary differential equations. In addition, we have formulated a flow grammar which is a grammatical characterization of flow patterns one may observe in phase spaces of ordinary differential equations.2. We have devised a new method of reasoning about qualitative behaviors which operates in both bottom-up and top-down mode. The bottom-up mode follows a prescribed procedure to collect information to capture the behavior. In contrast. the top-down mode is strongly guided by the domain knowledge, attempting to derive most plausible interpretation from partial information. In normal situations, the bottom-up mode is used, which will be switched to the top-down mode once logical failure is recognized.3. We have designed and implemented a prototype system called PSX2NL and have tested it against typical. examples to evaluate the method from experimental points of view.4. We have discussed about technical issues involved in a system which can analyze more complex ordinary differential equations with three unknowns. We have partly implemented the idea.