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DOI QR Code

GLOBAL STABILITY ANALYSIS FOR A CLASS OF COHEN-GROSSBERG NEURAL NETWORK MODELS

  • Guo, Yingxin
  • Received : 2009.11.22
  • Published : 2012.11.30

Abstract

By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability of the Cohen-Grossberg neural network models. The condition contains and improves some of the previous results in the earlier references.

Keywords

delay differential equations;Lyapunov functionals;matrix inequality;global asymptotic stability

References

  1. S. Arik, An analysis of global asymptotic stability of delayed cellular neural networks, IEEE Trans. Neural Networks 13 (2002), 1239-1242. https://doi.org/10.1109/TNN.2002.1031957
  2. P. Baldi and A. F. Atiya, How delays affect neural dynamics and learning, IEEE Trans Neural Networks 5 (1994), 612-621. https://doi.org/10.1109/72.298231
  3. J. Cao, On exponential stability and periodic solutions of CNNs with delays, Phys. Lett. A 267 (2000), no. 5-6, 312-318. https://doi.org/10.1016/S0375-9601(00)00136-5
  4. L. O. Chua and L. Yang, Cellular neural networks: theory and application, IEEE Trans. Circuits and Systems 35 (1988), no. 10, 1257-1272. https://doi.org/10.1109/31.7600
  5. P. P. Civalleri, M. Gilli, and L. Pandolfi, On stability of cellular neural networks with delay, IEEE Trans. Circuits Systems I Fund. Theory Appl. 40 (1993), no. 3, 157-165. https://doi.org/10.1109/81.222796
  6. M. A. Cohen and S. Grossberg, Absolute stability of global parallel memory storage by competitive neural networks, IEEE Trans Systems Man Cybermet 13 (1983), 815-826. https://doi.org/10.1109/TSMC.1983.6313075
  7. H. Jiang and Z. Teng, Global exponential stability of cellular neural networks with time-varying coefficients and delays, Neural Networks 17 (2004), 1415-1425. https://doi.org/10.1016/j.neunet.2004.03.002
  8. M. P. Kennedy and L. O. Chua, Neural networks for nonlinear programming, IEEE Trans. Circuits and Systems 35 (1988), no. 5, 554-562. https://doi.org/10.1109/31.1783
  9. Y. Li, Global exponential stability of BAM neural networks with delays and impulses, Chaos Solitons Fractals 24 (2005), no. 1, 279-285. https://doi.org/10.1016/j.chaos.2004.09.027
  10. T. L. Liao and F. C. Wang, Global stability for cellular neural networks with time delay, IEEE Trans. Neural Networks 11 (2000), 1481-1484. https://doi.org/10.1109/72.883480
  11. X. Liao and J. Wang, Global dissipativity of continuous-time recurrent neural networks with time delay, Phys. Rev. E (3) 68 (2003), no. 1, 016118, 7 pp. https://doi.org/10.1103/PhysRevE.68.016118
  12. Z. Liu and L. Liao, Existence and global exponential stability of periodic solution of cellular neural networks with time-varying delays, J. Math. Anal. Appl. 290 (2004), no. 1, 247-262. https://doi.org/10.1016/j.jmaa.2003.09.052
  13. C. M. Marcus and R. M. Westervelt, Stability of analog neural networks with delay, Phys. Rev. A (3) 39 (1989), no. 1, 347-359.
  14. M. Morita, Associative memory with nonmonotone dynamics, Neural Networks 6 (1993), 115-126. https://doi.org/10.1016/S0893-6080(05)80076-0
  15. T. Roska and L. O. Chua, Cellular neural networks with delay-type template elements nonuniform grid, Int J. Circuit Theory Appl 20 (1992), 469-481. https://doi.org/10.1002/cta.4490200504
  16. Q. Zhang, X. Wei, and J. Xu, A new global stability result for delayed neural networks, Nonlinear Anal. Real World Appl. 8 (2007), no. 3, 1024-1028. https://doi.org/10.1016/j.nonrwa.2006.06.002

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