Desynchronization of one-parameter families of stable vector fields

Abstract

Given a one-parameter family of vector fields on , Fλ(x), , such that for each λ, Fλ has a global asymptotically stable equilibrium point xλ, we construct a vector field on of the form G(λ, x) = (g(λ, x), Fλ(x)) which exhibits chaotic behaviour. This result is an incursion in the inverse problem of master–slave synchronization.This paper discusses self-disorganization of parameter dependent stable vector fields. Motivations are found in applications to drug design: one way to lead an unfriendly organism to death is to destabilize its metabolism. In this paper we envisage the mathematical aspect of the question. We show that for a very stable system (one globally attracting equilibrium state) depending on one parameter, there is a way for the system to act on the parameter so as to create chaos.