Cluster Synchronization in Uncertain Neural Networks Through Adaptive Controllers

Abstract

In this paper, we consider cluster synchronization in an uncertain generic neural network. The network is composed of many interactional clusters, including inner couplings in each cluster and outer couplings between different clusters. For the neural network, the dynamics of each cluster can be unknown and different. The coupling functions including uniform and nonuniform couplings between clusters can be unknown, too. By adding some time-varying linear and negative feedback controllers, we can guarantee that every cluster will synchronize at an arbitrary pre-assigned state/orbit of an isolated cluster of the network. Numerical simulations are presented to show the validity of the theoretical results.