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Pré-Publication, Document De Travail Année : 2011

Creating Chaos from a generic family of vector fields admitting a Hopf bifurcation

Camille Poignard
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Résumé

This text deals with the problem of creating a chaotic differential system from a generic one-parameter family of smooth vector fields on R^n, that exhibits a Hopf bifurcation, by imposing a dynamics on the parameter. We prove that if all the non purely imaginary eigenvalues of the Jacobian at the bifurcation point have a strictly negative real part, we can create such a chaotic system by inducing a hysteresis dynamics on it. After having presented the proof of this result, we illustrate it by showing how to induce a chaotic behavior in a four-dimensional differential system modeling the behavior of a hypothetical regulatory system.
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Dates et versions

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

Identifiants

  • HAL Id : hal-00586219 , version 1

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Camille Poignard. Creating Chaos from a generic family of vector fields admitting a Hopf bifurcation. 2011. ⟨hal-00586219v1⟩
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