Invariant manifolds and synchronization of coupled dynamical systems

Synchronization between coupled chaotic systems can be described in terms of invariant manifolds. If such manifolds possess the additional property of normal k-hyperbolicity, it can be deduced that synchronization will persist under perturbations. This suggests a mathematical framework within which the different aspects of synchronization can be discussed and analyzed. Using these techniques, it can be shown that unidirectionally and bidirectionally coupled synchronized systems are locally equivalent.