21734 articles – 15570 references  [version française]

inria-00367186, version 1

Limit cycles in piecewise-affine gene network models with multiple interaction loops

Etienne Farcot (Author to contact preferably) 1, Jean-Luc Gouzé () 2

N° RR-6875 (2009)

Abstract: In this paper we consider piecewise affine differential equations modeling gene networks. We work with arbitrary decay rates, and under a local hypothesis expressed as an alignment condition of successive focal points. The interaction graph of the system may be rather complex (multiple intricate loops of any sign, multiple thresholds...). Our main result is an alternative theorem showing that, if a sequence of region is periodically visited by trajectories, then under our hypotheses, there exists either a unique stable periodic solution, or the origin attracts all trajectories in this sequence of regions. This result extends greatly our previous work on a single negative feedback loop. We give several examples and simulations illustrating different cases.

  • 1:  Virtual Plants (VP)
  • Centre de coopération internationale en recherche agronomique pour le développement [CIRAD] : UMR51 – Institut national de la recherche agronomique (INRA) – INRIA
  • 2:  COMORE (INRIA Sophia Antipolis)
  • INRIA – CNRS : UMR7093
  • Domain : Mathematics/Dynamical Systems
    Life Sciences/Biochemistry, Molecular Biology/Molecular Networks
  • Keywords : piecewise linear dynamical systems – periodic trajectories – monotone – concave maps – interaction graph – genetic network models
  • Internal note : RR-6875
 
  • inria-00367186, version 1
  • http://hal.inria.fr/inria-00367186
  • oai:hal.inria.fr:inria-00367186
  • From: Etienne Farcot <>
  • Submitted on: Tuesday, 10 March 2009 15:27:50
  • Updated on: Wednesday, 11 March 2009 14:24:25