Analysis of synchronization of chaotic systems based on local conditional Lyapunov exponents

In this paper we consider the problem of synchronization of coupled chaotic systems. First we show the limitations of existing techniques for studying of the synchronization. Then we introduce the notion of local conditional (transversal) Lyapunov exponents. We show that they can be successfully used in investigations of synchronization properties. We develop a new criterion for synchronization based on local conditional Lyapunov exponents. The discussion is supported by numerical examples.