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DOI QR Code

NEW CONDITIONS ON EXISTENCE AND GLOBAL ASYMPTOTIC STABILITY OF PERIODIC SOLUTIONS FOR BAM NEURAL NETWORKS WITH TIME-VARYING DELAYS

  • Zhang, Zhengqiu (COLLEGE OF MATHEMATICS HUNAN UNIVERSITY) ;
  • Zhou, Zheng (COLLEGE OF MATHEMATICS HUNAN UNIVERSITY)
  • Received : 2009.07.01
  • Published : 2011.03.01

Abstract

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

Keywords

periodic solution;BAM neural networks;global asymptotic stability;coincidence degree theory;Lyapunov functional

References

  1. S. Arik, Global asymptotic stability analysis of bidirectional associative memory neural networks with time delays, IEEE Trans. Neural Networks 16 (2005), no. 3, 580-586. https://doi.org/10.1109/TNN.2005.844910
  2. S. Arik and V. Tavsanoglu, Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neurocomputing 68 (2005),161-176. https://doi.org/10.1016/j.neucom.2004.12.002
  3. J. D. Cao, Global asymptotic stability of delayed bi-directional associative memory neural networks, Appl. Math. Comput. 142 (2003), no. 2-3, 333-339. https://doi.org/10.1016/S0096-3003(02)00308-9
  4. J. D. Cao and Q. H. Jiang, An analysis of periodic solutions of bi-directional associative memory networks with time-varying delays, Phys. Lett. A 330 (2004), no. 3-4, 203-213. https://doi.org/10.1016/j.physleta.2004.07.064
  5. J. D. Cao and J. Q. Lu, Adaptive synchronization of neural networks with or without time-varying delay, Chaos 16 (2006), no. 1, 013133, 6 pp. https://doi.org/10.1063/1.2178448
  6. J. D. Cao and J. Wang, Global exponential stability and periodicity of recurrent neural networks with time delays, IEEE Trans. Circuits Syst. I Regul. Pap. 52 (2005), no. 5, 920-931. https://doi.org/10.1109/TCSI.2005.846211
  7. J. D. Cao and L.Wang, Periodic oscillatory solution of bidirectional associative memory networks with delays, Phys. Rev. E (3) 61 (2000), no. 2, 1825-1828. https://doi.org/10.1103/PhysRevE.61.1825
  8. J. D. Cao and L.Wang,Exiponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Trans. Neural Networks 13 (2002), no. 2, 457-463. https://doi.org/10.1109/72.991431
  9. J. D. Cao, K. Yuan, D. W. C. Ho, and J. Lam, Global point dissipativity of neural networks with mixed time-varying delays, Chaos 16 (2006), no. 1, 013105, 9 pp.
  10. A. P. Chen and F. L. Chen, Periodic solution to BAM neural network with delays on time scales, Neurocomputing 73 (2009), no. 1-3, 274-282. https://doi.org/10.1016/j.neucom.2009.08.013
  11. A. P. Chen, L. H. Huang, and J. D. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput. 137 (2003), no. 1, 177-193. https://doi.org/10.1016/S0096-3003(02)00095-4
  12. A. P. Chen, L. H. Huang, Z. G. Liu, and J. D. Cao, Periodic bidirectional associative memory neural networks with distributed delays, J. Math. Anal. Appl. 317 (2006), no. 1, 80-102. https://doi.org/10.1016/j.jmaa.2005.09.092
  13. C. H. Feng and R. Plamondon, Stability analysis of bidirectional associative memory networks with time delays, IEEE Trans. Neural Networks 14 (2003), no. 6, 1560-1565. https://doi.org/10.1109/TNN.2003.820829
  14. R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, Lecture Notes in Mathematics, Vol. 568. Springer-Verlag, Berlin-New York, 1977.
  15. K. Gopalsamy and X. Z. He, Delay-independent stability in bidirectional associative memory networks, IEEE Trans. Neural Networks 5 (1994), no. 6, 998-1002. https://doi.org/10.1109/72.329700
  16. B. Kosko, Bidirectional associative memories, IEEE Trans. Systems Man Cybernet. 18 (1988), no. 1, 49-60. https://doi.org/10.1109/21.87054
  17. C. D. Li, X. F. Liao, and R. Zhang, Delay-dependent exponential stability analysis of bi-directional associative memory neural networks with time delay: an LMI approach, Chaos, Solitons Fractals 24 (2005), no. 4, 1119-1134. https://doi.org/10.1016/j.chaos.2004.09.052
  18. J. L. Liang and J. D. Cao, Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays, Chaos, Solitons Fractals 22 (2004), no. 4, 773-785. https://doi.org/10.1016/j.chaos.2004.03.004
  19. X. F. Liao, K. W. Wong, and S. Z. Yuan, Convergence dynamics of hybrid bidirectional associative memory neural networks with distributed delays, Phys. Lett. A 316 (2003), no. 1-2, 55-64. https://doi.org/10.1016/S0375-9601(03)01113-7
  20. Z. G. Liu, A. P. Chen, J. D. Cao, and L. H. Huang, Existence and global exponential stability of periodic solution for BAM neural networks with periodic coefficients and time-varying delays, IEEE Trans. Circuits Systems I Fund. Theory Appl. 50 (2003), no. 9, 1162-1173. https://doi.org/10.1109/TCSI.2003.816306
  21. Z. G. Liu, A. P. Chen, and L. H. Huang, Existence and global exponential stability of periodic solution to self-connection BAM neural networks with delays, Phys. Lett. A 328 (2004), 127-143. https://doi.org/10.1016/j.physleta.2004.05.055
  22. Q. K. Song and Z. D. Wang, An analysis on existence and global exponential stability of periodic solutions for BAM neural networks with time-varying delays, Nonlinear Anal. Real World Appl. 8 (2007), no. 4, 1224-1234. https://doi.org/10.1016/j.nonrwa.2006.07.002

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