JOURNAL BROWSE
Search
Advanced SearchSearch Tips
EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS
Liu Bingwen; Huang Lihong;
  PDF(new window)
 Abstract
In this paper cellular neural networks with continuously distributed delays are considered. Sufficient conditions for the existence and exponential stability of the almost periodic solutions are established by using fixed point theorem, Lyapunov functional method and differential inequality technique. The results of this paper are new and they complement previously known results.
 Keywords
cellular neural networks;almost periodic solution;exponential stability;continuously distributed delays;
 Language
English
 Cited by
1.
Linear attraction in quasi-linear difference systems, Journal of Difference Equations and Applications, 2011, 17, 05, 765  crossref(new windwow)
2.
Existence and stability of almost periodic solutions in impulsive neural network models, Applied Mathematics and Computation, 2010, 217, 8, 4167  crossref(new windwow)
3.
Global exponential stability of a class of neural networks with unbounded delays, Ukrainian Mathematical Journal, 2008, 60, 10, 1633  crossref(new windwow)
4.
ASYMPTOTIC EQUIVALENCE OF ALMOST PERIODIC SOLUTIONS FOR A CLASS OF PERTURBED ALMOST PERIODIC SYSTEMS, Glasgow Mathematical Journal, 2010, 52, 03, 583  crossref(new windwow)
 References
1.
A. Berman and R. J. Plemmons, Nonnegative matrices in the mathematical sci- ences, 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 crossref(new window)

3.
J. Cao, New results concering exponential stability and periodic solutions of de- layed cellular neural networks, Phys. Lett. A 307 (2003), no. 2-3, 136-147 crossref(new window)

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 crossref(new window)

5.
A. Chen and L. H. Huang, Existence and attractivity of almost periodic solutions of Hopfield neural networks, (Chinese) 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 crossref(new window)

7.
A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974

8.
S. Guo and L. Huang, Periodic solutions in an inhibitory two-neuron network, J. Comput. Appl. Math. 161 (2003), no. 1, 217-229 crossref(new window)

9.
S. Guo and L. Huang, Stability analysis of a delayed Hopfield neural network, Phys. Rev. E (3) 67 (2003), no. 6, 061902, 7 pp crossref(new window)

10.
J. Hale and S. M. Verduyn Lunel, Introduction to functional-differential equations, Applied Mathematical Sciences, 99. Springer-Verlag, New York, 1993

11.
C. Y. He, Almost periodic differential equation, Higher Education Publishing House, Beijin, 1992. [In Chinese]

12.
X. Huang and J. Cao, Almost periodic solutions of inhibitory cellular neural networks with with time-vary delays, Phys. Lett. A 314 (2003), no. 3, 222-231 crossref(new window)

13.
H. Huang, J. Cao, and J.Wang, Global exponential stability and periodic solutions of recurrent cellular neural networks with delays, Phys. Lett. A 298 (2002), no. 5-6, 393-404 crossref(new window)

14.
J. P. Lasalle, The stability of dynamical systems, Regional Conference Series in Applied Mathematics. SIAM, Philadelphia, 1976

15.
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 crossref(new window)

16.
Z. Liu and L. Liao, Existence and global exponential stability of periodic solutions of cellular neural networks with time-vary delays, J. Math. Anal. Appl. 290 (2004), no. 1, 247-262 crossref(new window)