Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

  • Liu Bingwen (College of Mathematics and Information Science Jiaxing University) ;
  • Huang Lihong (College of Mathematics and Econometrics Hunan University)
  • Published : 2006.03.01
Download PDF
⟨ Previous Next ⟩

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

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 https://doi.org/10.1006/jcss.1999.1658
  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 https://doi.org/10.1016/S0375-9601(02)01720-6
  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 https://doi.org/10.1016/S0096-3003(01)00274-0
  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 https://doi.org/10.1016/S0362-546X(01)00113-4
  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 https://doi.org/10.1016/j.cam.2003.08.002
  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 https://doi.org/10.1103/PhysRevE.67.061902
  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 https://doi.org/10.1016/S0375-9601(03)00918-6
  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 https://doi.org/10.1016/S0375-9601(02)00537-6
  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 https://doi.org/10.1016/j.physleta.2003.10.020
  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 https://doi.org/10.1016/j.jmaa.2003.09.052

Cited by

  1. ASYMPTOTIC EQUIVALENCE OF ALMOST PERIODIC SOLUTIONS FOR A CLASS OF PERTURBED ALMOST PERIODIC SYSTEMS vol.52, pp.03, 2010, https://doi.org/10.1017/S0017089510000443
  2. Global exponential stability of a class of neural networks with unbounded delays vol.60, pp.10, 2008, https://doi.org/10.1007/s11253-009-0155-7
  3. Linear attraction in quasi-linear difference systems vol.17, pp.05, 2011, https://doi.org/10.1080/10236190903260820
  4. Existence and stability of almost periodic solutions in impulsive neural network models vol.217, pp.8, 2010, https://doi.org/10.1016/j.amc.2010.10.033