Inducing chaos in a gene regulatory network by coupling an oscillating dynamics with a hysteresis-type one. - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2012

Inducing chaos in a gene regulatory network by coupling an oscillating dynamics with a hysteresis-type one.

Camille Poignard
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Résumé

In this paper, we investigate the chaotic behavior of a gene regulatory network modeled by four differential equations and seventeen parameters. This network, called V-system, has been designed to couple in a simple way an oscillating system with one having a bistable switch. After having studied it analytically, we exhibit (by a constructive proof) the mechanism responsible of chaos for a general differential system presenting such a coupling. Namely, given a generic one-parameter family of smooth vector fields on R^n presenting a Hopf bifurcation, we prove that under an assumption on the Jacobian at the bifurcation point, we can create such a chaotic system by perturbing the parameter thanks to a hysteresis-type dynamics. Finally, we numerically show that the mechanism highlighted previously takes place in the V-system, for a particular set of values of its parameters.
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Dates et versions

hal-00586219 , version 1 (15-04-2011)
hal-00586219 , version 2 (04-05-2012)

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  • HAL Id : hal-00586219 , version 2

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Camille Poignard. Inducing chaos in a gene regulatory network by coupling an oscillating dynamics with a hysteresis-type one.. 2012. ⟨hal-00586219v2⟩
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