Estimates of equilibrium points and global asymptotic stability of Cohen–Grossberg neural networks with delays

This article studies a class of Cohen–Grossberg neural networks (CGNNs) with variable and distributed delays. Some novel conditions guaranteeing the existence, uniqueness and the estimated location of the equilibrium points are obtained. Using these results, the global asymptotic stability of the CGNNs can be derived without demanding the boundedness and the globally Lipschitz condition of the activation functions. Two numerical examples are demonstrated to verify the theoretical results.

[1]  Qiankun Song,et al.  Global exponential robust stability of Cohen-Grossberg neural network with time-varying delays and reaction-diffusion terms , 2006, J. Frankl. Inst..

[2]  Tianping Chen,et al.  Global Asymptotical Stability of Cohen-Grossberg Neural Networks with Time-Varying and Distributed Delays , 2006, ISNN.

[3]  Dao-Yi Xu,et al.  Invariant and attracting sets of Hopfield neural networks with delay , 2001, Int. J. Syst. Sci..

[4]  Jinde Cao,et al.  Stability in delayed Cohen–Grossberg neural networks: LMI optimization approach , 2005 .

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

[6]  J. Cao,et al.  LMI-based criteria for globally robust stability of delayed Cohen–Grossberg neural networks , 2006 .

[7]  Jinde Cao,et al.  Global exponential stability of discrete-time Cohen-Grossberg neural networks , 2005, Neurocomputing.

[8]  Jinde Cao,et al.  Absolutely exponential stability of Cohen-Grossberg neural networks with unbounded delays , 2005, Neurocomputing.

[9]  Jinde Cao,et al.  Stability in Cohen–Grossberg-type bidirectional associative memory neural networks with time-varying delays , 2006 .

[10]  Jinde Cao,et al.  Periodic Oscillation of Fuzzy Cohen-Grossberg Neural Networks with Distributed Delay and Variable Coefficients , 2008, J. Appl. Math..

[11]  Hongyong Zhao,et al.  Dynamics of Cohen–Grossberg neural networks with variable and distributed delays , 2007 .

[12]  Leon O. Chua,et al.  Stability analysis of generalized cellular neural networks , 1993, Int. J. Circuit Theory Appl..

[13]  Réjean Plamondon,et al.  On the stability analysis of delayed neural networks systems , 2001, Neural Networks.

[14]  Daoyi Xu,et al.  Global attraction and stability for Cohen-Grossberg neural networks with delays , 2006, Neural Networks.

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

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

[17]  Stephen Grossberg,et al.  Absolute stability of global pattern formation and parallel memory storage by competitive neural networks , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[18]  Qian Jixin,et al.  Stability analysis for neural dynamics with time-varying delays , 1998, IEEE Trans. Neural Networks.

[19]  Jinde Cao,et al.  New conditions for global exponential stability of cellular neural networks with delays , 2005, Neural Networks.

[20]  Shumin Fei,et al.  Stability analysis of Cohen-Grossberg neural networks with time-varying and distributed delays , 2008, Neurocomputing.

[21]  B. Cui,et al.  Global asymptotic stability of Cohen–Grossberg neural networks with constant and variable delays , 2007 .

[22]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[23]  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.

[24]  Leon O. Chua,et al.  Neural networks for nonlinear programming , 1988 .

[25]  Xinghua Wang,et al.  Exponential stability of impulsive Cohen–Grossberg networks with distributed delays , 2008, Int. J. Circuit Theory Appl..

[26]  Chuandong Li,et al.  Stability of Cohen-Grossberg neural networks with unbounded distributed delays , 2007 .

[27]  Jianhua Sun,et al.  Global asymptotic stability of Cohen–Grossberg neural network with continuously distributed delays , 2005 .

[28]  Jinde Cao,et al.  Global exponential stability of Hopfield neural networks , 2001, Int. J. Syst. Sci..

[29]  Jianhua Sun,et al.  Global exponential stability and periodic solutions of Cohen–Grossberg neural networks with continuously distributed delays , 2005 .

[30]  Xuyang Lou,et al.  Global exponential stability analysis of delayed Cohen--Grossberg neural networks with distributed delays , 2007, Int. J. Syst. Sci..