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

Etienne Farcot 1, * Jean-Luc Gouzé 2
* Corresponding author
1 VIRTUAL PLANTS - Modeling plant morphogenesis at different scales, from genes to phenotype
CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique, UMR AGAP - Amélioration génétique et adaptation des plantes méditerranéennes et tropicales
2 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
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.
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https://hal.inria.fr/inria-00367186
Contributor : Etienne Farcot <>
Submitted on : Tuesday, March 10, 2009 - 3:27:50 PM
Last modification on : Thursday, March 4, 2021 - 3:25:11 PM
Long-term archiving on: : Tuesday, June 8, 2010 - 11:19:30 PM

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  • HAL Id : inria-00367186, version 1
  • ARXIV : 0903.1969

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Etienne Farcot, Jean-Luc Gouzé. Limit cycles in piecewise-affine gene network models with multiple interaction loops. [Research Report] RR-6875, INRIA. 2009. ⟨inria-00367186⟩

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