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

Authors:
Lili Wang;Tianping Chen
Affiliations:
Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, PR China;School of Computer Sciences, Key Laboratory of Nonlinear Mathematics Science, School of Mathematical Sciences, Fudan University, Shanghai, PR China
Venue:
Neural Networks
Year:
2012

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Abstract

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 3^n equilibrium points. Then, we track the dynamics of u(t)(t0) in two cases with respect to different types of subset regions in which u(0) is located. It concludes that every solution trajectory 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.