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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00586219
Contributor : Camille Poignard Connect in order to contact the contributor
Submitted on : Friday, May 4, 2012 - 6:07:49 PM
Last modification on : Monday, October 12, 2020 - 10:27:33 AM

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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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