Complete stability of cellular neural networks with unbounded time-varying delays

In this paper, we are concerned with the delayed cellular neural networks (DCNNs) in the case that the time-varying delays are unbounded. Under some conditions, it shows that the DCNNs can exhibit 3n3n equilibrium points. Then, we track the dynamics of u(t)(t>0)u(t)(t>0) in two cases with respect to different types of subset regions in which u(0)u(0) is located. It concludes that every solution trajectory u(t)u(t) would converge to one of the equilibrium points despite the time-varying delays, that is, the delayed cellular neural networks are completely stable. The method is novel and the results obtained extend the existing ones. In addition, two illustrative examples are presented to verify the effectiveness of our results.