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 3(n) equilibrium points. Then, we track the dynamics of u(t)(t>0) 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.

[1]  Leon O. Chua,et al.  Pattern formation properties of autonomous Cellular Neural Networks , 1995 .

[2]  Tianping Chen,et al.  Multistability and New Attraction Basins of Almost-Periodic Solutions of Delayed Neural Networks , 2009, IEEE Transactions on Neural Networks.

[3]  Zhang Yi,et al.  Multistability of discrete-time recurrent neural networks with unsaturating piecewise linear activation functions , 2004, IEEE Transactions on Neural Networks.

[4]  Leon O. Chua,et al.  Cellular neural networks: applications , 1988 .

[5]  Tianping Chen,et al.  Power-Rate Global Stability of Dynamical Systems With Unbounded Time-Varying Delays , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  Lin-Bao Yang,et al.  Cellular neural networks: theory , 1988 .

[7]  Zhigang Zeng,et al.  Complete Stability of Cellular Neural Networks With , 2006 .

[8]  Chih-Wen Shih,et al.  Complete Stability in Multistable Delayed Neural Networks , 2009, Neural Computation.

[9]  Tianping Chen,et al.  Coexistence and local stability of multiple equilibria in neural networks with piecewise linear nondecreasing activation functions , 2010, Neural Networks.

[10]  Wei Xing Zheng,et al.  A New Method for Complete Stability Analysis of Cellular Neural Networks With Time Delay , 2010, IEEE Transactions on Neural Networks.

[11]  Tianping Chen,et al.  On Attracting Basins of Multiple Equilibria of a Class of Cellular Neural Networks , 2011, IEEE Transactions on Neural Networks.

[12]  Jinde Cao,et al.  Multistability of Second-Order Competitive Neural Networks With Nondecreasing Saturated Activation Functions , 2011, IEEE Transactions on Neural Networks.

[13]  Tianping Chen,et al.  Global $\mu$ -Stability of Delayed Neural Networks With Unbounded Time-Varying Delays , 2007, IEEE Transactions on Neural Networks.

[14]  Jin Xu,et al.  An improved result for complete stability of delayed cellular neural networks , 2005, Autom..

[15]  Shun-ichi Amari,et al.  New theorems on global convergence of some dynamical systems , 2001, Neural Networks.

[16]  Eva Kaslik,et al.  Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis , 2011, Neural Networks.

[17]  Norikazu Takahashi,et al.  Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  Derong Liu,et al.  Cellular neural networks for associative memories , 1993 .