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Neural Processing Letters

, Volume 39, Issue 3, pp 247–268 | Cite as

Existence and Global Exponential Stability of Almost Periodic Solution for High-Order BAM Neural Networks with Delays on Time Scales

  • Yongkun Li
  • Chao Wang
  • Xia Li
Article

Abstract

In this paper, by using a fixed point theorem and by constructing a suitable Lyapunov functional, we study the existence and global exponential stability of almost periodic solution for high-order bidirectional associative memory neural networks with delays on time scales. An examples shows the feasibility of our main results.

Keywords

Almost periodic solution High-order BAM neutral networks Time scales Global exponential stability 

Notes

Acknowledgments

This work is supported by the National Natural Sciences Foundation of People’s Republic of China under Grant 10971183 and this work was also supported by IRTSTYN.

References

  1. 1.
    Wu C, Ruan J, Lin W (2006) On the existence and stability of the periodic solution in the Cohen–Grossberg neural network with time delay and high-order terms. Appl Math Comput 177:194–210CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Ren F, Cao J (2007) Periodic solutions for a class of higher-order Cohen–Grossberg type neural networks with delays. Comput Math Appl 54:826–839CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Yu Y, Cai M (2008) Existence and exponential stability of almost-periodic solutions for high-order Hopfield neural networks. Math Comput Model 47:943–951CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Zhang J, Gui Z (2009) Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays. J Comput Appl Math 224:602–613CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Chen Z, Zhao D, Fu X (2009) Discrete analogue of high-order periodic Cohen–Grossberg neural networks with delay. Appl Math Comput 214:210–217CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Xiao B, Meng H (2009) Existence and exponential stability of positive almost periodic solutions for high-order Hopfield neural networks. Appl Math Model 33:532–542CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Li YK, Zhao L, Liu P (2009) Existence and exponential stability of periodic solution of high-order Hopfield neural network with delays on time scales. Discret Dyn Nat Soc. Article ID 573534Google Scholar
  8. 8.
    Wang L (2010) Existence and global attractivity of almost periodic solutions for delayed high-ordered neural networks. Neurocomputing 73:802–808CrossRefGoogle Scholar
  9. 9.
    Liu Q, Xu R (2011) Periodic solutions of high-order Cohen–Grossberg neural networks with distributed delays. Commun Nonlinear Sci Numer Simul 16:2887–2893CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Nie X, Cao J (2011) Multistability of second-order competitive neural networks with nondecreasing saturated activation functions. IEEE Trans Neural Netw 22:1694–1708CrossRefGoogle Scholar
  11. 11.
    Nie X, Cao J (2012) Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions. Neurocomputing 82:1–13CrossRefGoogle Scholar
  12. 12.
    Li YK, Chen XR, Zhao L (2009) Stability and existence of periodic solutions to delayed Cohen–Grossberg BAM neural networks with impulses on time scales. Neurocomputing 72:1621–1630CrossRefGoogle Scholar
  13. 13.
    Li YK, Yang L, Wu WQ (2011) Anti-periodic solutions for a class of Cohen–Grossberg neutral networks with time-varying delays on time scales. Int J Syst Sci 42:1127–1132CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Li YK, Zhang TW (2009) Global exponential stability of fuzzy interval delayed neural networks with impulses on time scales. Int J Neural Syst 19(6):449–456CrossRefGoogle Scholar
  15. 15.
    Li YK, Gao S (2010) Global exponential stability for impulsive BAM neural networks with distributed delays on time scales. Neural Process Lett 31(1):65–91Google Scholar
  16. 16.
    Li YK, Wang C (2012) Almost periodic solutions of shunting inhibitory cellular neural networks on time scales. Commun Nonlinear Sci Numer Simul 17:3258–3266CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Teng Z (2002) Nonautonomous Lotka–Volterra systems with delays. J Differ Equ 179:538–561CrossRefzbMATHGoogle Scholar
  18. 18.
    Xu B, Yuan R (2005) The existence of positive almost periodic type solutions for some neutral nonlinear integral equation. Nonlinear Anal 60:669–684CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Liu B, Huang L (2008) Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 9:830–841CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Bohner M, Peterson A (2001) Dynamic equations on time scales. An introduction with applications. Birkhäuser, BostonCrossRefzbMATHGoogle Scholar
  21. 21.
    Bohner M, Peterson A (2003) Advances in dynamic equations on time scales. Birkhäuser, BostonCrossRefzbMATHGoogle Scholar
  22. 22.
    Li YK, Wang C (2011) Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales. Abstr Appl Anal. Article ID 341520Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsYunnan UniversityKunmingPeople’s Republic of China

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