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A Class of Piecewise Linear Differential Equations Arising in Biological Models

Jean-Luc Gouzé 1 Tewfik Sari
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
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Submitted on : Wednesday, May 24, 2006 - 9:54:10 AM
Last modification on : Thursday, March 10, 2022 - 5:58:02 PM
Long-term archiving on: : Sunday, April 4, 2010 - 11:06:37 PM


  • HAL Id : inria-00072415, version 1


Jean-Luc Gouzé, Tewfik Sari. A Class of Piecewise Linear Differential Equations Arising in Biological Models. RR-4207, INRIA. 2001. ⟨inria-00072415⟩



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