Synchronization in Ring Networks of Systems with Transmission Delays*

This paper investigates synchronization phenomena that occur in ring networks of identical chaotic systems with delays. In particular, we focus on delay-independent synchronization of systems in ring networks with transmission delays. First, we show that ring networks consisting of an odd number of systems emerge full synchronization for coupling strengths larger than a certain value independently on the size of time-delay Next, we also show that if the number of systems in ring networks is even, then partial synchronization can be observed regardless of the size of time-delay In this case, full synchronization may also be observed as a special case of partial synchronization. Numerical examples show the validity of these theoretical results.