Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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GLOBAL EXPONENTIAL STABILITY OF BAM NEURAL NETWORKS WITH IMPULSES AND DISTRIBUTED DELAYS

  • Shao, Yuanfu (School of Mathematics and Computer Science, Guizhou Normal University) ;
  • Luo, Zhenguo (School of Mathematical Sciences and Computing Technology, Central South University)
  • Received : 2010.03.28
  • Accepted : 2010.06.21
  • Published : 2011.01.30
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Abstract

By using an important lemma, some analysis techniques and Lyapunov functional method, we establish the sufficient conditions of the existence of equilibrium solution of a class of BAM neural network with impulses and distributed delays. Finally, applications and an example are given to illustrate the effectiveness of the main results.

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References

  1. Y.H. Xia, J.D. Cao and M.R. Lin, New results on the existence and uniqueness of almost periodic solutions for BAM neural networks with continuously distributed delays, Chaos Solit. Fract. 314 (2007) 928-936.
  2. J.D. Cao, Global asymptotic stability of delayed bi-directional associative memory neural networks, Appl. Math. Comput. 142 (2003) 333-339. https://doi.org/10.1016/S0096-3003(02)00308-9
  3. J.D. Cao, Exponential stability of delayed bi-directional associative memory neural networks, Appl. Math. Comput. 135 (2003) 105-112. https://doi.org/10.1016/S0096-3003(01)00315-0
  4. A.P. Chen, L.H. Huang, Z.G. Liu and J.D. Cao, Periodic bi-directional associative memory neural networks with distributed delays, J. Math. Anal. Appl. 317 (2006) 80-102. https://doi.org/10.1016/j.jmaa.2005.09.092
  5. H. Wang, X.F. Liao and C.D. Li, Existence and exponential stability of periodic solution of BAM neural networks with impulse and time varying delays, Chaos Solit. Fract. 33 (2007) 1028-1039. https://doi.org/10.1016/j.chaos.2006.01.112
  6. W.C.daniel, J.L. Liang and L.James, Global exponential stability of impulsive high-order BAM neural networks with time varying delays, Neural Networks, 19 (2006) 1581-1590. https://doi.org/10.1016/j.neunet.2006.02.006
  7. Arik Sabri and T.Vedat, Global asymptotic stability analysis of bidirectional associative memory neural networks with constant time delays, Neucomputing 68 (2005) 161-176.
  8. R.C. Wu, Exponential convergence of BAM neural networks with time-varying coefficients and distributed delays, doi:10.1016/j.nonrwa.2009.02.003.
  9. J. Chen and B.T. Cui, Impulsive effects on global asymptotic stability of delay BAM neural networks, Chaos Solit. Fract. 38 (2008) 1115-1125. https://doi.org/10.1016/j.chaos.2007.01.042
  10. Q.H. Zhou, Global exponential stability of BAM neural networks with distributed delays and impulses, Nonlinear Anal. RWA 10 (2009) 144-153. https://doi.org/10.1016/j.nonrwa.2007.08.019
  11. Z.K. Huang and Y.H. Xia, Exponential periodic attractor of impulsive BAM networks with finite distributed delays, Chaos Solit. Fract. 39 (2009) 373-384. https://doi.org/10.1016/j.chaos.2007.04.014
  12. H.Q. Wu and C.H. Shan, Stability analysis for periodic solution of BAM neural networks with discontinuous neuron activations and impulses, Appl. Math. Model. 33 (2009) 2564-2574. https://doi.org/10.1016/j.apm.2008.07.022
  13. Z. Gui and W. Ge, Existence and uniqueness of periodic solutions of nonautonomous cellular neural networks with impulses, Phys. Lett. A 354 (2006) 84-94. https://doi.org/10.1016/j.physleta.2006.01.018
  14. C.Z. Bai, Global exponential stability and existence of periodic solution of Cohen-Grossberg type neural networks with delays and impulses, Nonlinear Anal. RWA 9 (2008) 747-761. https://doi.org/10.1016/j.nonrwa.2006.12.007
  15. X.S. Yang, Existence and global exponential stability of periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks with delays and impulses, doi:10.1016/j.neucom. 2009.01.003.
  16. H.B. Gu, H.J. Jiang and Z.D. Teng, Existence and globally exponential stability of periodic solution of BAM neural networks with impulses and recent-history distributed delays, Neurocomputing, 71 (2008) 813-822. https://doi.org/10.1016/j.neucom.2007.03.007
  17. Y.T. Li and J.Y. Wang, An analysis on the global exponential stability and the existence of periodic solutions for non-autonomous hybrid BAM neural networks with distributed delays and impulses, Comput. Math. Appl. 56 (2008) 2256-2267. https://doi.org/10.1016/j.camwa.2008.03.048
  18. Z. Gui and W. Ge, Periodic solutions of nonautonomous cellular neural networks with impulses, Chaos Solit. Fract. 32 (2007) 1760-1771. https://doi.org/10.1016/j.chaos.2005.12.001
  19. J. Zhang and Z. Gui, Periodic solutions of nonautonomous cellular neural networks with impulses and delays, Nonlinear Anal. 10 (2009) 1891-1903. https://doi.org/10.1016/j.nonrwa.2008.02.029
  20. Y.K. Li, Global exponential stability of BAM neural networks with delays and impulses, Chaos Solit. Fract. 24 (2005) 279-285.
  21. H.Y. Zhao, Global stability of bidirectional associative memory neural networks with dis- tributed delays, Phys. Lett. A 297 (2002) 182-190. https://doi.org/10.1016/S0375-9601(02)00434-6
  22. B. Liu and L. Huang, Global exponential stability of BAM neural networks with recent-history distributed delays and impulses, Neucomputing 69 (2006) 2090-2096.
  23. Y.H. Xia, Z.K. Huang and M.A. Han, Existence and globally exponential stability of equilibrium for BAM neural networks with impulses, Chaos Solit. Fract. 37 (2008) 588-597. https://doi.org/10.1016/j.chaos.2006.08.045
  24. S. Mohamad, K. Gopalsamy and H. Acka, Exponential stability of artificial neural networks with distributed delays and large impulses, Nonl. Anal. RWA 9 (2008) 872-888. https://doi.org/10.1016/j.nonrwa.2007.01.011
  25. Z.K. Huang and Y.H. Xia, Global exponential stability of BAM neural networks with transmission delays and nonlinear impulses, Chaos Solit. Frac. 38 (2008) 489-498. https://doi.org/10.1016/j.chaos.2006.11.032
  26. Y.H. Xia and Patr.Y. Wong, Global exponential stability of a class of retarded impulsive differential equations with applications, Chaos Solit. Fract. bf39 (2009) 440-453.
  27. R. Samidurai, R. Sakthivel and S.M. Anthoni, Global asymptotic stability of BAM neural networks with mixed delays and impulses, doi:10.1016/j.amc.2009.02.002.
  28. Richard and s. Varga, Matrix Iterative Analysis, Springer Press, 2004.
  29. B. Fang, J. Zhou and Y. Li, Matrix Theory, Tinghua University Press and Springer Press, 2004.
  30. Q. Zhang, X. Wei and J. Xu, Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays, Chaos Solit. Fract. 36 (2008) 985-990. https://doi.org/10.1016/j.chaos.2006.07.034
  31. M. Forti and A. Tesi, New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans. Circuit. syst. I 42 (1995) 354-366. https://doi.org/10.1109/81.401145