Synchronization of chaotic systems by using occasional coupling

We present a method for the synchronization of chaotic systems by using occasional coupling. In this method we assume that a chaotic drive system and a response system to be synchronized with the drive system are given. We also assume that a scheme that results in exponentially fast synchronization is available (full synchronization). Then we present an occasional-coupling scheme in which the drive and response systems are coupled in some intervals (synchronization phases) and decoupled in some intervals (autonomous phases), i.e., the response system is switched to an autonomous system. We prove that if the lengths of these intervals are appropriately chosen, then under some mild conditions synchronization can be achieved. We also show that the proposed scheme is robust with respect to noise and parameter mismatch under some mild conditions.