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inria-00072415, version 1

A Class of Piecewise Linear Differential Equations Arising in Biological Models

Jean-Luc Gouzé () 1, Tewfik Sari

N° RR-4207 (2001)

Résumé : We investigate the properties of the solutions of a class of piecewise-linear differential equations. The equations are appropriate to model biological systems in which there are switch-like interactions between the elements of the network. The analysis uses the concept of Filippov solutions of discontinuous righthand sides equations. It gives an insight on the so-called singular solutions which lie on the surfaces of discontinuity. We study several examples of genetic networks.

  • 1 :  COMORE (INRIA Sophia Antipolis)
  • INRIA – CNRS : UMR7093
  • Domaine : Informatique/Autre
  • Mots-clés : DISCONTINUOUS DIFFERENTIAL EQUATIONS / STEADY STATES / FILIPPOV SOLUTIONS / STABILITY / BIOLOGICAL SYSTEMS / GENETIC NETWORKS
  • Référence interne : RR-4207
 
  • inria-00072415, version 1
  • http://hal.inria.fr/inria-00072415
  • oai:hal.inria.fr:inria-00072415
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  • Soumis le : Mercredi 24 Mai 2006, 09:54:10
  • Dernière modification le : Mercredi 31 Mai 2006, 14:24:26