Exponential Stability of Cohen-Grossberg Neural Networks with Delays

The exponential stability characteristics of the Cohen-Grossberg neural networks with discrete delays are studied in this paper, without assuming the symmetry of connection matrix as well as the monotonicity and differentiability of the activation functions and the self-signal functions. By constructing suitable Lyapunov functionals, the delay-independent sufficient conditions for the networks converge exponentially toward the equilibrium associated with the constant input are obtained. It does not doubt that our results are significant and useful for the design and applications of the Cohen-Grossberg neural networks.

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

[2]  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.

[3]  Guanrong Chen,et al.  Novel robust stability criteria for interval-delayed Hopfield neural networks , 2001 .

[4]  Wang,et al.  Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Stephen Grossberg,et al.  Nonlinear neural networks: Principles, mechanisms, and architectures , 1988, Neural Networks.

[6]  V. Sree Hari Rao,et al.  Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones , 1999, Neural Networks.

[7]  Jinde Cao,et al.  Global asymptotic stability of a general class of recurrent neural networks with time-varying delays , 2003 .

[8]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[9]  K. Gopalsamy,et al.  Stability in asymmetric Hopfield nets with transmission delays , 1994 .

[10]  Xiaofeng Liao,et al.  Novel stability criteria for bidirectional associative memory neural networks with time delays , 2002, Int. J. Circuit Theory Appl..

[11]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[12]  Kwok-Wo Wong,et al.  Novel stability conditions for Cellular Neural Networks with Time Delay , 2001, Int. J. Bifurc. Chaos.

[13]  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.

[14]  Xiaofeng Liao,et al.  Robust stability for interval Hopfield neural networks with time delay , 1998, IEEE Trans. Neural Networks.

[15]  Pauline van den Driessche,et al.  Global Attractivity in Delayed Hopfield Neural Network Models , 1998, SIAM J. Appl. Math..

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

[17]  Juebang Yu,et al.  Qualitative analysis of Bi‐directional Associative Memory with time delay , 1998 .

[18]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[19]  X. Zou,et al.  Harmless delays in Cohen–Grossberg neural networks ☆ , 2002 .

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

[22]  Mark P. Joy,et al.  Results concerning the absolute stability of delayed neural networks , 2000, Neural Networks.

[23]  X. Liao,et al.  Stability analyses of cellular neural networks with continuous time delay , 2002 .

[24]  Jinde Cao,et al.  Global Exponential Stability of Cohen-Grossberg Neural Networks with Multiple Time-Varying Delays , 2004, ISNN.