Strong generalized synchronization with a particular relationship R between the coupled systems

Abstract

The question of the chaotic synchronization of two coupled dynamical systems is an issue that interests researchers in many elds, from biology to psychology, through economics, chemistry, physics, and many others. The di erent forms of couplings and the di erent types of synchronization, give rise to many problems, most of them little studied. In this paper we deal with general couplings of two dynamical systems and we study strong generalized synchronization with a particular relationship R between them. Our results include the de nition of a window in the domain of the coupling strength, where there is an exponentially stable solution, and the explicit determination of this window. In the case of unidirectional or symmetric couplings, this window is presented in terms of the maximum Lyapunov exponent of the systems. Examples of applications to chaotic systems of dimension one and two are presented.