Qualitative Simulation of Differential Equations

Aubin, J.-P. (1988). Qualitative Simulation of Differential Equations. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-88-015

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Abstract

This paper deals with the QSIM algorithm introduced by Kuipers to track down the changes of monotonicity properties of solutions to a differential equation or other observations of the solutions. It introduces the concept of "qualitative cells" where the monotonicity properties of the states of the system remain the same. It provides sufficient conditions for the non-emptiness of such cells, for their singularities, for the transition from one cell to another, and characterizes also the qualitative equilibria and repellors of the associated qualitative system.

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