Synchronized chaotic systems: theory and applications to nonlinear oscillator networks

Abstract

Synchronized chaotic systems have received much attention in recent years as an example of systems that exhibit regularity at the "global" level while existing in seeming disorder "locally". The synchronization of chaotic oscillators forming a network is a topic of special interest, with a wide range of applicability. Here we review the basic theory and then apply it to a network of Lorenz systems. We also propose a method of improving the synchronizability of a network by choosing a form of coupling that makes the associated network tensor possess hyperbolicity for weak coupling.