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Kuiper's QSIM algorithm is an expert system which studies thequalitative evolution of a differential inclusion. This paper addressesseveral issues raised by QSIM-type algorithms attached to landmarkvalues, by using the concept of QQqualitative cells/Q/Q. Only thesystems which share the same behavior on the boundary between two cellscan be analyzed qualitatively. The principal purpose of this paper is toassociate with a differential equation its QQqualitative projection/Q/Qwhich assigns to each qualitative cell its QQsuccessors/Q/Q, to show howthis algorithm can be implemented, and to illustrate the results withQQreplicator systems/Q/Q: a class of differential equation used inbiochemistry and biology.—Author's Abstract