DOI QR코드

DOI QR Code

EXISTENCE AND EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTION FOR SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS AND LARGE IMPULSES

  • Zuo, Yi (COLLEGE OF ELECTRIC AND INFORMATION TECHNOLOGY HUNAN UNIVERSITY, DEPARTMENT OF APPLIED MATHEMATICS UNIVERSITY OF WATERLOO) ;
  • Wang, Yaonan (COLLEGE OF ELECTRIC AND INFORMATION TECHNOLOGY HUNAN UNIVERSITY) ;
  • Huang, Lihong (COLLEGE OF MATHEMATICS AND ECONOMETRICS HUNAN UNIVERSITY) ;
  • Li, Chunsheng (COLLEGE OF ELECTRIC AND INFORMATION TECHNOLOGY HUNAN UNIVERSITY)
  • Published : 2009.09.01

Abstract

This paper considers the problem of existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with distributed delays and large impulses. Based on the contraction principle and Gronwall-Bellman's inequality, some sufficient conditions are obtained. The results of this paper are new and they complement previously known results.

Keywords

References

  1. D. Bainov and P. Simeonov, Theory of Impulsive Differential Equations: Periodic Solutions and Applications, Harlow: Longman, 1993
  2. A. Bouzerdoum and R. Pinter, Shunting inhibitory cellular neural networks: derivation and stability analysis, IEEE Trans. Circuits Systems I Fund. Theory Appl. 40 (1993), no. 3, 215.221 https://doi.org/10.1109/81.222804
  3. J. Cao, A. Chen, and X. Huang, Almost periodic attractor of delayed neural networks with variable coefficients, Physics Letters A 340 (2005), no. 1-4, 104.120 https://doi.org/10.1016/j.physleta.2005.04.021
  4. J. Cao, P. Li, and W.Wang, Global synchronization in arrays of delayed neural networks with constant and delayed coupling, Physics Letters A 353 (2006), no. 4, 318.325 https://doi.org/10.1016/j.physleta.2005.12.092
  5. J. Cao and X. Li, Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach, Phys. D 212 (2005), no. 1-2, 54.65 https://doi.org/10.1016/j.physd.2005.09.005
  6. J. Cao, J. Liang, and J. Lam, Exponential stability of high-order bidirectional associative memory neural networks with time delays, Phys. D 199 (2004), no. 3-4, 425.436 https://doi.org/10.1016/j.physd.2004.09.012
  7. J. Cao and J. Lu, Adaptive synchronization of neural networks with or without timevarying delay, Chaos 16 (2006), no. 1, 261.266 https://doi.org/10.1063/1.2178448
  8. A. Chen and J. Cao, Almost periodic solution of shunting inhibitory CNNs with delays, Phys. Lett. A 298 (2002), no. 2-3, 161.170 https://doi.org/10.1016/S0375-9601(02)00469-3
  9. L. Chua and L. Yang, Cellular neural networks: theory, IEEE Trans. Circuits and Systems 35 (1988), no. 10, 1257.1272 https://doi.org/10.1109/31.7600
  10. L. Chua and L. Yang, Cellular neural networks: applications, IEEE Trans. Circuits and Systems 35 (1988), no. 10, 1273.1290 https://doi.org/10.1109/31.7601
  11. 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. https://doi.org/10.1016/S0375-9601(03)00918-6
  12. V. Lakshmikantham, D. Bainov, and P. Simeonov, Theory of impulsive differential equations, Singapore: World Scientific, 1989
  13. Y. Li, C. Liu, and L. Zhu, Global exponential stability of periodic solution for shunting inhibitory CNNs with delays, Physics Letters A 337 (2005), no. 3, 40.54 https://doi.org/10.1016/j.physleta.2005.01.008
  14. Y. Li, W. Xing, and L. Lu, Existence and global exponential stability of periodic solution of a class of neural networks with impulses, Chaos Solitons Fractals 27 (2006), no. 2, 437.445 https://doi.org/10.1016/j.chaos.2005.04.021
  15. X. Liu and G. Ballinger, Existence and continuability of solutions for differential equations with delays and state-dependent impulses, Nonlinear Anal. 51 (2002), no. 4, Ser. A: Theory Methods, 633.647 https://doi.org/10.1016/S0362-546X(01)00847-1
  16. X. Liu and G. Ballinger, Uniform asymptotic stability of impulsive delay differential equations, Comput. Math. Appl. 41 (2001), no. 7-8, 903.915 https://doi.org/10.1016/S0898-1221(00)00328-X
  17. B. Liu and L. Huang, Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays, Physics Letters A 349 (2006), no. 1, 177.186 https://doi.org/10.1016/j.physleta.2005.09.023
  18. Y. Liu, Z. You, and L. Cao, On the almost periodic solution of generalized shunting inhibitory cellular neural networks with continuously distributed delays, Physics Letters A 360 (2006), no. 1, 122.130 https://doi.org/10.1016/j.physleta.2006.08.013
  19. Y. Liu, Z. You, and L. Cao, Almost periodic solution of shunting inhibitory cellular neural networks with time-varying and continuously distributed delays, Physics Letters A 364 (2007), no. 1, 17.28 https://doi.org/10.1016/j.physleta.2006.11.075
  20. A. Samoilenko and N. Perestyuk, Differential Equations with Impulses Effect, Visca Skola: Kiev, 1987
  21. H. Shen, Global existence and uniqueness, oscillation, and nonoscillation of impulsive delay differential equations, Acta Math. Sinica (Chin. Ser.) 40 (1997), no. 1, 53.59
  22. Y. Xia, Positive periodic solutions for a neutral impulsive delayed Lotka-Volterra competition system with the effect of toxic substance, Nonlinear Anal. Real World Appl. 8 (2007), no. 1, 204.221 https://doi.org/10.1016/j.nonrwa.2005.07.002
  23. Y. Xia and J. Cao, Almost periodicity in an ecological model with M-predators and N-preys by “pure-delay type” system, Nonlinear Dynam. 39 (2005), no. 3, 275.304 https://doi.org/10.1007/s11071-005-4006-2
  24. Y. Xia and J. Cao, Almost-periodic solutions for an ecological model with infinite delays, Proc. Edinb. Math. Soc. (2) 50 (2007), no. 1, 229.249 https://doi.org/10.1017/S0013091504001233
  25. Y. Xia, J. Cao, and Z. Huang, Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Chaos Solitons Fractals 34 (2007), no. 5, 1599.1607 https://doi.org/10.1016/j.chaos.2006.05.003
  26. Y. Xia, J. Cao, and M. Lin, Existence and exponential stability of almost periodic solution for BAM neural networks with impulse, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 13A (2006), Part 1, suppl., 248.255
  27. Y. Xia, J. Cao, and M. Lin, New results on the existence and uniqueness of almost periodic solution for BAM neural networks with continuously distributed delays, Chaos Solitons Fractals 31 (2007), no. 4, 928.936 https://doi.org/10.1016/j.chaos.2005.10.043
  28. J. Yan, Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model, J. Math. Anal. Appl. 279 (2003), no. 1, 111.120. https://doi.org/10.1016/S0022-247X(02)00613-3
  29. J. Yan, J. Zhao, and W. Yan, Existence and global attractivity of periodic solutionfor an impulsive delay differential equation with Allee effect, J. Math. Anal. Appl. 309 (2005), no. 2, 489.504. https://doi.org/10.1016/j.jmaa.2004.09.038
  30. Q. Zhou, B. Xiao, Y. Yu, and L. Peng, Existence and exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays, Chaos Solitons Fractals 34 (2007), no. 3, 860.866 https://doi.org/10.1016/j.chaos.2006.03.092