Bipartite synchronization criterion for coupled neural networks with pining control

In this paper, we discuss the anti-synchronization problem of coupled neural networks with time-varying delay, which is also known as the bipartite synchronization problem. Different from the existing literature, the competitive relationship in coupled neural networks is considered, which can be modeled by a signed graph. Due to the signed topology structure, bipartite synchronization is realized when all states of coupled neural networks converge to a final state with identical magnitude but opposite sign. Under the structurally balanced assumption, a pining control scheme is designed and then the bipartite synchronization criterion for coupled neural networks with time-varying delay is obtained. Finally, we present a numerical example to demonstrate the validity of the obtained results