Robust synchronization of chaotic systems

The question of robustness of synchronization with respect to small arbitrary perturbations of the underlying dynamical systems is addressed. We present examples of chaos synchronization demonstrating that normal hyperbolicity is a necessary and sufficient condition for the synchronization manifold to be smooth and persistent under small perturbations. The same examples, however, show that in real applications normal hyperbolicity is not sufficient to give quantitative bounds for deformations of the synchronization manifold, i.e., even in the case of normal hyperbolicity two almost identical systems may cause large synchronization errors.