Browse > Article
http://dx.doi.org/10.4134/JKMS.2007.44.4.873

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

Liu, Bingwan (DEPARTMENT OF MATHEMATICS HUNAN UNIVERSITY OF ARTS AND SCIENCE)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 873-887 More about this Journal
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;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 J. Hale and S. M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, 99. Springer-Verlag, New York, 1993
2 Z. Liu, A. Chen, J. Cao, and L. Huang, Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays, Phys. Lett. A 319 (2003), no. 3-4, 305-316   DOI   ScienceOn
3 Z. Liu and L. Liao, Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays, J. Math. Anal. Appl. 290 (2004), no. 1, 247-262   DOI   ScienceOn
4 A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Science, Academic Press, New York, 1979
5 J. Cao, Global exponential stability and periodic solutions of delayed cellular neural networks, J. Comput. System Sci. 60 (2000), no. 1, 38-46   DOI   ScienceOn
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   DOI   ScienceOn
7 A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377. Springer-Verlag, Berlin-New York, 1974
8 C. Y. He, Almost periodic differential equation, Higher Education Publishing House, Beijing, 1992
9 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   DOI   ScienceOn
10 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   DOI   ScienceOn
11 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
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   DOI   ScienceOn
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   DOI   ScienceOn
14 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   DOI   ScienceOn
15 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   DOI   ScienceOn