Robust synchronization of chaotic systems

The question of robustness of synchronization with respect to small arbitra ry perturbations of the underlying dynamical systems is addressed. We prese nt examples of chaos synchronization demonstrating that normal hyperbolicit y is a necessary and sufficient condition for the synchronization manifold to be smooth and persistent under small perturbations. The same examples, h owever, show that in real applications normal hyperbolicity is not sufficie nt to give quantitative hounds for deformations of the synchronization mani fold, i.e., even in the case of normal hyperbolicity two almost identical s ystems may cause large synchronization errors.