Creating Chaos from a generic family of vector fields admitting a Hopf bifurcation
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.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)