EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITHOUT GLOBAL LIPSCHITZ CONDITIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 44, Issue 4, 2007, pp.873-887
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2007.44.4.873

Title & Authors

EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITHOUT GLOBAL LIPSCHITZ CONDITIONS

Liu, Bingwan;

Liu, Bingwan;

Abstract

In this paper cellular neutral networks with time-varying delays and continuously distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using the fixed point theorem and differential inequality techniques. The results of this paper are new and complement previously known results.

Keywords

cellular neural networks;almost periodic solution;exponential stability;fixed point theorem;delays;

Language

English

Cited by

References

1.

A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Science, Academic Press, New York, 1979

2.

J. Cao, Global exponential stability and periodic solutions of delayed cellular neural networks, J. Comput. System Sci. 60 (2000), no. 1, 38-46

3.

J. Cao, New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Phys. Lett. A 307 (2003), no. 2-3, 136-147

4.

A. Chen and J. Cao, Existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients, Appl. Math. Comput. 134 (2003), no. 1, 125-140

5.

A. Chen and L. H. Huang, Existence and attractivity of almost periodic solutions of Hopfield neural networks, Acta Math. Sci. Ser. A Chin. Ed. 21 (2001), no. 4, 505-511

6.

Q. Dong, K. Matsui, and X. Huang, Existence and stability of periodic solutions for Hopfield neural network equations with periodic input, Nonlinear Anal. 49 (2002), no. 4, Ser. A: Theory Methods, 471-479

7.

A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377. Springer-Verlag, Berlin-New York, 1974

8.

J. Hale and S. M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, 99. Springer-Verlag, New York, 1993

9.

C. Y. He, Almost periodic differential equation, Higher Education Publishing House, Beijing, 1992

10.

X. Huang and J. Cao, Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delay, Phys. Lett. A 314 (2003), no. 3, 222-231

11.

H. Huang, J. Cao, and J. Wang, Global exponential stability and periodic solutions of recurrent neural networks with delays, Phys. Lett. A 298 (2002), no. 5-6, 393-404

12.

B. Liu and L. Huang, Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays, Phys. Lett. A 341 (2005), 135-144

13.

B. Liu and L. Huang, Existence and exponential stability of almost periodic solutions for Hopfield neural networks with delays, Neurocomputing 68 (2005), 196-207