2n Almost Periodic Attractors for Cohen-Grossberg Neural Networks with Variable and Distribute Delays

In this paper, we investigate dynamics of 2n almost periodic attractors for Cohen-Grossberg neural networks (CGNNs) with variable and distribute time delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CGNNs into 2n compact convex subsets. Then the existence of 2n almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder-s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2n almost periodic solutions and exponential attracting domains are also given correspondingly.

• Meng Hu
• Lili Wang

• CGNNs
• almost periodic solution
• invariant basins
• attracting domains.

[1] M.A. Cohen, S. Grossberg, Absolute stability of global pattern formation
and parallel memory storage by competitive neural network, IEEE
Transactions on Systems, Man, and Cybernetics 13 (5) (1983) 815-826.
[2] S. Guo, L. Huang, Stability analysis of Cohen-Grossberg neural networks,
IEEE Transactions on Neural Networks 17 (1) (2006) 106-117.
[3] Y. Chen, Global asymptotic stability of delayed Cohen-Grossberg neural
network, IEEE Transactions on Circuits and Systems I: Regular Papers
53 (2) (2006) 351-357.
[4] J. Cao, J. Liang, Boundedness and stability for Cohen-Grossberg neural
networks with time-varying delays, J. Math. Anal. Appl. 296 (2) (2004)
665-685.
[5] W. Su, Y. Chen, Global robust stability criteria of stochastic Cohen-
Grossberg neural networks with discrete and distributed time-varying
delays, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 520-528.
[6] Z. Orman, S. Arik, New results for global stability of Cohen-Grossberg
neural networks with multiple time delays, Neurocomputing 71 (2008)
3053-3063.
[7] Y. Meng, S. Guo, L. Huang, Convergence dynamics of Cohen-Grossberg
neural networks with continuously distributed delays, Appl. Math. Comput.
202 (2008) 188-199.
[8] C. Lien, K. Yu, Y. Lin, Y. Chung, L. Chung, Stability conditions for
Cohen-Grossberg neural networks with time-varying delays, Phys. Lett.
A 372 (2008) 2264-2268.
[9] T. Huang, A. Chan, Y. Huang, J. Cao, Stability of Cohen-Grossberg neural
networks with time-varying delays, Neural Networks 20 (2007) 868-873.
[10] W. Wu, B. Cui, X. Lou, Global exponential stability of Cohen-Grossberg
neural networks with distributed delays, Math. Comput. Modell. 47 (2008)
868-873.
[11] A.M. Fink, Almost Periodic Differential Equation, Springer-Verlag,
Berlin, Heidleberg, New York, 1974.
[12] C.Y. He, Almost Periodic Differential Equations, Higher Education
Publishing House, Beijing, 1992 (in Chinese).
[13] Y. Li, X. Fan, Existence and globally exponential stability of almost periodic
solution for Cohen-Grossberg BAM neural networks with variable
coefficients, Appl. Math. Modell. (2008), doi:10.1016/j.apm.2008.05.013.
[14] Y. Xia, J. Cao, Almost periodic solution of Cohen-Grossberg neural
networks with bounded and unbounded delays, Nonlinear Anal. RWA
(2008), doi:10.1016/j.nonrwa.2008.04.021.
[15] H. Zhao, L. Chen, Z. Mao, Existence and stability of almost periodic
solution for Cohen-Grossberg neural networks with variable coefficients,
Nonlinear Anal. RWA 9(2) (2008) 663-673.
[16] Z. Huang, S. Mohamad, G. Cai, 2N almost periodic attractors for CNNs
with variable and distributed delays, J. Franklin Institute 346 (2009) 391-
412.