Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

[1]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[2]  K. Gopalsamy Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[3]  X. Lou,et al.  Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2006 .

[4]  Xue-Zhong He,et al.  Delay-independent stability in bidirectional associative memory networks , 1994, IEEE Trans. Neural Networks.

[5]  Zhigang Zeng,et al.  Complete stability of cellular neural networks with time-varying delays , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Zhang Qiang,et al.  Global exponential convergence analysis of delayed cellular neural networks , 2003 .

[7]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[8]  Xiaofeng Liao,et al.  (Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach , 2002, Neural Networks.

[9]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[10]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[11]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of neural networks with time-varying delays , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Tan Wen,et al.  Synchronization of an uncertain chaotic system via recurrent neural networks , 2005 .

[13]  Jinde Cao A set of stability criteria for delayed cellular neural networks , 2001 .

[14]  S. Arik,et al.  On the global asymptotic stability of delayed cellular neural networks , 2000 .

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

[16]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

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

[18]  Hongtao Lu Chaotic attractors in delayed neural networks , 2002 .

[19]  Lin Wang,et al.  Exponential stability of Cohen-Grossberg neural networks , 2002, Neural Networks.

[20]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of chaotic neural networks , 2005 .

[21]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[22]  Jinde Cao Global stability conditions for delayed CNNs , 2001 .

[23]  Yu Juebang,et al.  ANALYSIS OF STABILITY FOR EQUILIBRIUM OFCELLULAR NEURAL NETWORKS , 2001 .

[24]  Wei Wu,et al.  Some criteria for asymptotic stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neurocomputing.

[25]  M. Gilli Strange attractors in delayed cellular neural networks , 1993 .