Mathematical problems arising in qualitative simulation of a differential equation

摘要

Kuiper's QSIM algorithm is an expert system which studies the qualitative evolution of a differential inclusion. This paper addresses several issues raised by QSIM-type algorithms attached to landmark values, by using the concept of QQqualitative cells/Q/Q. Only the systems which share the same behavior on the boundary between two cells can be analyzed qualitatively. The principal purpose of this paper is to associate with a differential equation its QQqualitative projection/Q/Q which assigns to each qualitative cell its QQsuccessors/Q/Q, to show how this algorithm can be implemented, and to illustrate the results with QQreplicator systems/Q/Q: a class of differential equation used in biochemistry and biology.