Nonlinear integral synchronization of ring networks

It is generally difficult to synchronize a ring network that features single nearest-neighbor coupling, if the number N of nodes of the network is too large. In this paper, we consider a ring network of N identical nodes, which are unidirectionally coupled through the first state variable of each node. We present a new nonlinear integral method for synchronization of such a network, and derive a sufficient condition for synchronization of this type of network with chaotic nodes. The entire ring network will synchronize by adding only one nonlinear integral feedback, even if the feedback gain is very small. As examples, we study the synchronization of such a network with Lorenz system nodes and Chua's system nodes. Our numerical simulations confirm the effectiveness of the new method.