Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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PERIODIC SOLUTION TO DELAYED HIGH-ORDER COHEN-GROSSBERG NEURAL NETWORKS WITH REACTION-DIFFUSION TERMS

  • Lv, Teng (Teaching and Research Section of Computer, Artillery Academy) ;
  • Yan, Ping (College of Mathematics and System Science, Xinjiang University)
  • Published : 2010.01.30
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Abstract

In this paper, we study delayed high-order Cohen-Grossberg neural networks with reaction-diffusion terms and Neumann boundary conditions. By using inequality techniques and constructing Lyapunov functional method, some sufficient conditions are given to ensure the existence and convergence of the periodic oscillatory solution. Finally, an example is given to verify the theoretical analysis.

Keywords

References

  1. M. Cohen, S. Grossberg, Absolute stability and global pattern formation and parallel memory storagy by competitive neural networks, IEEE Trans. Syst. Man Cybernet SMC-13(1983), 15-23.
  2. J. Cao, L. Liang, Boundedness and stability for Coheb-Grossbery neural network withtime- varying delays, J.Math. Anal.Application 296(2004), 665-685. https://doi.org/10.1016/j.jmaa.2004.04.039
  3. J. Cao, X. Li, Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach, Physica D 212(2005), 54-65. https://doi.org/10.1016/j.physd.2005.09.005
  4. Z. Chen, H. Zhao & J. Ruan, Dynamic analysis of high-order Cohen-Grossberg neural networks with time delay, Chaos Solitons & Fractals 24(2006), 421-430.
  5. H. Jiang, J. Cao, Dynamics of Cohen-Grossbery neural networks with time-varying delays, Phys. Lett.A 354(2006), 414-422. https://doi.org/10.1016/j.physleta.2006.01.078
  6. T. Chen, L. Rong, Robust global exponential stability of Cohen-Grossberg neural networks with time delays, IEEE trans. Neur. Network 15(2004), 203-206. https://doi.org/10.1109/TNN.2003.822974
  7. Y. Li, Existence and stability of periodic solutions for Cohen-Grossbery neural networks with multiple delays, Chaos Solitons & Fractals 20(2004), 459-466. https://doi.org/10.1016/S0960-0779(03)00406-5
  8. C. Hwang, C. Cheng & T. Li, Globally exponential stability of generalized Cohen-Grossberg neural networks with time dilay, Phys. Lett. A 319(2003), 157-166. https://doi.org/10.1016/j.physleta.2003.10.002
  9. H. Wan, H. Qiao & J. Peng, Delay-independent criteria for exponential stability generalized Cohen-Grossberg neural networks with dicrete delay, Phys. Lett.A 353(2006), 151-157. https://doi.org/10.1016/j.physleta.2005.12.085
  10. X. Liao, C. Li & K. Wong, Criteria for exponential stability of Cohe-Crossberg neural networks, Neural Networks 17(2004), 1401-1414. https://doi.org/10.1016/j.neunet.2004.08.007
  11. W. Xiong, D. Xu, Global exponential stability of discrete-time Cohen-Grossberg neural networks, Neurocomputing 64(2005), 433-446. https://doi.org/10.1016/j.neucom.2004.08.004
  12. J. Xu, Z. Liu,& X. Liao, Global asymptotic stability of high-order Hopfield type neural networks with time delays, Comp. Math. Application 45(2003), 1729-1737. https://doi.org/10.1016/S0898-1221(03)00151-2
  13. P.Yan, T. Lv, Stavility of delayed reaction diffusion high-order Cohen-Grossberg neural networks with variable coefficient, Proccedings of Second International Symposium on Intelligent Information Technology Application, IEEE CS Press 1(2008), 741-745.
  14. K. Yuan, J. Cao, Global exponential stability of Cohen-Grossberg networks with multiple time-barying delays, LNCS 3173(2004), 745-753.
  15. J. Zhang, Y. Suda, H. Komine, Global exponential Stability of Cohen-Grossbery neural networks with variable delays, Phys. Lett.A 338(2005), 44-50. https://doi.org/10.1016/j.physleta.2005.02.005
  16. H. Zhao, K. Wang, Dynamical behaviors of Cohen-Grosberg neural networks with delays and reaction-diffusion terms, Neurocomputing 70(2006), 536-543. https://doi.org/10.1016/j.neucom.2005.11.009
  17. J. Cao, L. Liang & J. Lamb, Exponenial Stability of high-order bidirectional associative memory neural networks with time delays, Physica D 199(2004), 425-436. https://doi.org/10.1016/j.physd.2004.09.012
  18. J. Liang, J. Cao, Global exponential Stability of reaction- diffusion recurrent neural networks with time- varying delays, Phys. Lett. A 314(2003), 434-442. https://doi.org/10.1016/S0375-9601(03)00945-9
  19. Q. Song, J. Cao, , Global exponential Stability and existence of periodic solutions in BAM neural networks with distributed delays and reaction-diffusion terms, Chaos Solitons & Fracctals 23(2005), 421-430. https://doi.org/10.1016/j.chaos.2004.04.011
  20. Q. Song, Z. Zhao, Y. Li, Global exponential Stability of BAM neural networks with distributed delays and reaction-diffusion terms, Phys. Lett. A 335 (2005), 213-225. https://doi.org/10.1016/j.physleta.2004.12.007
  21. Q. Song, J. Cao, Z. Zhao, Periodic solutions and its exponential stability of reaction-diffusion recurrent neural netwokes with continuously distributed delays, Nonlinear Anal :Real World Application 7(2006), 421-430.
  22. H. Zhao, G. Wang, Existence of periodic oscillatory solution of reaction-diffusion neural networks with delays, Phys. Lett. A 343(2005), 372-383. https://doi.org/10.1016/j.physleta.2005.05.098
  23. G. Lu, Global exponential Stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet Boundary conditons, Chaos Solitons & Fractals 35(2008), 116-125. https://doi.org/10.1016/j.chaos.2007.05.002
  24. S. Schiff, K. Jerger, D. Duong, etc, Controlling chaos in the brain, Nature 370(1994), 615-620. https://doi.org/10.1038/370615a0
  25. X. Liao, K. Wong, C. Leung, etc, Hopf bifurcation and chaos in a single delayed neuron equation with non monotonic activation function, Chaos Solitons & Fractals 12 (2001), 1535-1547. https://doi.org/10.1016/S0960-0779(00)00132-6