Synchronization in unidirectional ring network of chaotic systems with delay-coupling

In this paper, we consider the synchronization problem in unidirectional ring networks of chaotic systems with time-delay coupling. Firstly, we introduce the notion of strict semi-dissipativity and show by using the small-gain theorem that the trajectories of coupled systems satisfying the strict semi-dissipativity are bounded. Then we derive a sufficient condition for synchronization of the systems coupled in a unidirectional way by using a stability criterion for delay systems