Mathematical problems arising in qualitative simulation of a differential equation

✍ Scribed by Olivier Dordan

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 938 KB
• Volume: 55
• Category: Article
• ISSN: 0004-3702
• DOI: 10.1016/0004-3702(92)90042-v

✦ Synopsis

Dordan, O., Mathematical problems arising in qualitative simulation of a differential equation, Artificial Intelligence 55 (1992) 61-86.

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.