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GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS OF HIGH-ORDER HOPFIELD NEURAL NETWORKS WITH DISTRIBUTED DELAYS OF NEUTRAL TYPE

  • Zhao, Lili (Department of Mathematics, Yunnan University) ;
  • Li, Yongkun (Department of Mathematics, Yunnan University)
  • Received : 2012.07.20
  • Accepted : 2012.11.07
  • Published : 2013.05.30

Abstract

In this paper, we study the global stability and the existence of almost periodic solution of high-order Hopfield neural networks with distributed delays of neutral type. Some sufficient conditions are obtained for the existence, uniqueness and global exponential stability of almost periodic solution by employing fixed point theorem and differential inequality techniques. An example is given to show the effectiveness of the proposed method and results.

References

  1. Y.K. Li, L. Zhao and P. Liu, Existence and exponential stability of periodic solution of high-order Hopfield neural network with delays on time scales, Discrete Dyamics in Nature and Society 2009 (2009), Article ID573534, 18pages.
  2. S. Mohamad, Exponential stability in Hopfield-type neural networks with impuses, Chaos Solitons Fractals 32 (2007), 456-467. https://doi.org/10.1016/j.chaos.2006.06.035
  3. B. J. Xu and X. Z. Liu, Global asymptotic stability of high-order Hopfield type neurual networks with time delays, Comput. Math. Appl. 45 (2003), 1279-1737.
  4. E.B. Kosmatopoulos and M.A. Christodoulou, Structural properties of gradient recurrent high-order neural networks, IEEE Trans. Circuits Syst. II 42 (1995), 592-603. https://doi.org/10.1109/82.466645
  5. X. Lou and B. Cui, Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays, J. Math. Anal. Appl. 330 (2007), 144-158. https://doi.org/10.1016/j.jmaa.2006.07.058
  6. B. Xiao and H Meng, Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks, Appl. Math. Modelling 33 (2009), 532-542. https://doi.org/10.1016/j.apm.2007.11.027
  7. Y. Yu and M. Cai, Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks, Math. Comput. Modelling 47 (2008), 943-951. https://doi.org/10.1016/j.mcm.2007.06.014
  8. B. Xu, X. Liu and X. Liao, Global exponential stability of high order Hopfield type neural networks, Appl. Math. Comput. 174 (2006), 98-116. https://doi.org/10.1016/j.amc.2005.03.020
  9. C.Z. Bai, Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays, Appl. Math. Comput. 203 (2008), 72-79. https://doi.org/10.1016/j.amc.2008.04.002
  10. B. Xu, X. Liu and K.L. Teo, Global exponential stability of impulsive high-order Hopfield type neural networks with delays, Comput. Math. Appl. 57 (2009), 1959-1967. https://doi.org/10.1016/j.camwa.2008.10.001
  11. P. Shi and L. Dong, Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses, Appl. Math. Comput. 216 (2010), 623-630. https://doi.org/10.1016/j.amc.2010.01.095
  12. J. Li, J. Yang and W. Wu, Stability and periodicity of discrete Hopfield neural networks with column arbitrary-magnitude-dominant weight matrix, Neurocomputing 82 (2012), 52-61. https://doi.org/10.1016/j.neucom.2011.10.025
  13. J.H. Park, O.M. Kwon and S.M. Lee, LMI optimization approach on stability for delayed neural networks of neutral-type, Appl. Math. Comput. 196 (2008), 236-244. https://doi.org/10.1016/j.amc.2007.05.047
  14. J.H. Park, C.H. Park, O.M. Kwon and S.M. Lee, A new stability criterion for bidirectional associative memory neural networks of neutral-type, Appl. Math. Comput. 199 (2008) 716-722. https://doi.org/10.1016/j.amc.2007.10.032
  15. S.M. Lee, O.M. Kwon and J.H. Park, A novel delay-dependent criterion for delayed neural networks of neutral type, Phys. Lett. A 374 (2010), 1843-1848. https://doi.org/10.1016/j.physleta.2010.02.043
  16. Y.K. Li, L. Zhao and X.R. Chen, Existence of periodic solutions for neutral type cellular neural networks with delays, Appl. Math. Modelling 36 (2012), 1173-1183. https://doi.org/10.1016/j.apm.2011.07.090
  17. S. Mandal and N.C. Majee, Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays, Neurocomputing 74 (2011), 1000-1007. https://doi.org/10.1016/j.neucom.2010.11.021
  18. K. Wang and Y. Zhu, Stability of almost periodic solution for a generalized neutral-type neural networks with delays, Neurocomputing 73 (2010), 3300-3307. https://doi.org/10.1016/j.neucom.2010.05.017
  19. S. Mandal and N.C. Majee, Existence of periodic solutions for a class of Cohen-Grossberg type neural networks with neutral delays, Neurocomputing 74 (2011), 1000-1007. https://doi.org/10.1016/j.neucom.2010.11.021
  20. A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, vol. 377, Springer, Berlin, 1974.
  21. C. Y. He, Almost Periodic Differential Equations, Higher Education Publishing House, Beijing, 1992 (in Chinese).