Delay-independent Synchronization in Ring Networks of Identical/Non-identical Systems with Transmission Delay Couplings

Department of Mechanical Engineering, Graduate School of Science & Engineering Tokyo Metropolitan University 1-1 Minami-Osawa, Hachioji-shi, Tokyo 192-0397 Japan

^* Corresponding author. E-mail: t.oguchi@tmu.ac.jp

Abstract

This paper investigates synchronization phenomena occurring in networks of chaotic systems with delays. In particular, we focus on delay-independent synchronization in ring networks of systems with transmission delays. First, we show that all the systems in ring networks consisting of an odd number of systems synchronize for any constant 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 length of time-delay. In this case, full synchronization may also be observed as a special case of partial synchronization. In addition, we show that if two different dynamical systems are alternately arranged in even-sized ring networks, synchronization occurs among systems with the identical dynamics for any time-delay. Numerical examples show the validity of these theoretical results.