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Comparative envisionment construction: A technique for the comparative analysis of dynamical systems. (English) Zbl 0996.00013
Summary: In many situations it is desirable to compare the behaviors of two dynamical systems, in order to (i) predict consequences of differential initial conditions or (ii) find causes of differential responses. CEC* is a qualitative reasoning technique for solving such comparative analysis (CA) problems. Using propagation constraints implied by the models and behaviors of the systems, it generates comparative envisionments describing their differential dynamics in a qualitative manner. CEC* improves upon existing CA approaches in a number of ways. It addresses within a single framework CA problems involving systems with different models and behaviors, it handles ambiguities caused by the qualitative nature of the analysis, it reasons from differences in the initial conditions to differences in the response, as well as the other way round, and it is not limited to a restricted class of problems due to the possibility to derive appropriate propagation constraints from the models and behaviors. CEC* has been implemented and tested on a dozen of simple and more complex systems, in which it had to answer CA questions involving several differences in the models and initial conditions. CEC* is firmly rooted in the theory of differential equations, which allows definitions and proofs of formal properties of the algorithm. In particular, it has been shown that CEC* is sound and incomplete.

MSC:
00A71 General theory of mathematical modeling
34C99 Qualitative theory for ordinary differential equations
37C99 Smooth dynamical systems: general theory
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