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Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays

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Abstract

In this paper, a nonautonomous impulsive neutral-type neural network with delays is considered. By establishing a singular impulsive delay differential inequality and employing contraction mapping principle, several sufficient conditions ensuring the existence and global exponential stability of the periodic solution for the impulsive neutral-type neural network with delays are obtained. Our results can extend and improve earlier publications. An example is given to illustrate the theory.

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References

  1. Zhao, H.: Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays. Appl. Math. Comput. 154, 683–695 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhao, H.: Global exponential stability and periodicity of cellular neural networks with variable delays. Phys. Lett. A 336, 331–341 (2005)

    Article  MATH  Google Scholar 

  3. Zhao, H., Chen, L., Mao, Z.: Existence and stability of almost periodic solution for Cohen-Grossberg neural networks with variable coefficients. Nonlinear Anal. 9, 663–673 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Huang, X., Cao, J., Daniel, W.C.: Existence and attractivity of almost periodic solution for recurrent neural networks with unbounded delays and variable coefficients. Nonlinear Dyn. 45, 337–351 (2006)

    Article  MATH  Google Scholar 

  5. Wang, L., Gao, Y.: Global exponential robust stability of reaction-diffusion interval neural networks with S-type distributed time-varying delays. Phys. Lett. A 5–6, 342–348 (2006)

    Article  Google Scholar 

  6. Wang, L., Cao, J.: Global robust point dissipativity of interval neural networks with mixed time-varying delays. Nonlinear Dyn. 55, 169–178 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Wang, L., Zhang, R., Wang, Y.: Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays. Nonlinear Anal. 10, 1101–1113 (2009)

    Article  MATH  Google Scholar 

  8. Qiu, J., Cao, J.: Delay-dependent robust stability of neutral-type neural networks with time delays. J. Math. Cont. Sci. Appl. 1, 179–188 (2007)

    Google Scholar 

  9. Cao, J., Zhong, S., Hu, Y.: Global stability analysis for a class of neural networks with time varying delays and control input. Appl. Math. Comput. 189, 1480–1490 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Bai, C.: Global stability of almost periodic solutions of Hopfield neural networks with neutral time-varying delays. Appl. Math. Comput. 203, 72–79 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gui, Z., Ge, W., Yang, X.: Periodic oscillation for a Hopfield neural networks with neutral delays. Phys. Lett. A 364, 267–273 (2007)

    Article  MATH  Google Scholar 

  12. Park, J.H., Kwon, O.M., Lee, S.M.: LMI optimization approach on stability for delayed neural networks of neutral-type. Appl. Math. Comput. 196, 236–244 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Park, J.H., Kwon, O.M., Lee, S.M.: State estimation for neural networks of neutral-type with interval time-varying delay. Appl. Math. Comput. 203, 217–223 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Park, J.H., Park, C.H., Kwon, O.M., Lee, S.M.: A new stability criterion for bidirectional associative memory neural networks of neutral-type. Appl. Math. Comput. 199, 716–722 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Park, J.H., Kwon, O.M.: Design of state estimator for neural networks of neutral-type. Appl. Math. Comput. 202, 360–369 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rakkiyappan, R., Balasubramaniam, P.: New global exponential stability results for neutral type neural networks with distributed time delays. Neurocomputing 71, 1039–1045 (2008)

    Article  Google Scholar 

  17. Rakkiyappan, R., Balasubramaniam, P.: LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays. Appl. Math. Comput. 204, 317–324 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)

    MATH  Google Scholar 

  19. Arbib, M.: Branins, Machines, and Mathematics. Springer, New York (1987)

    Google Scholar 

  20. Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice-Hall, Englewood Cliffs, New Jersey (1998)

    Google Scholar 

  21. Xu, D., Yang, Z.: Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305, 107–120 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  22. Yang, Z., Xu, D.: Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays. Appl. Math. Comput. 177, 63–78 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yang, Z., Xu, D.: Existence and exponential stability of periodic solution for impulsive delay differential equations and applications. Nonlinear Anal. 64, 130–145 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  24. Xu, D., Yang, Z., Yang, Z.: Exponential stability of nonlinear impulsive neutral differential equations with delays. Nonlinear Anal. 67, 1426–1439 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Weng, A., Sun, J.: Globally exponential stability of periodic solutions for nonlinear impulsive delay systems. Nonlinear Anal. 67, 1938–1946 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  26. Xia, Y., Cao, J., Cheng, S.: Global exponential stability of delayed cellular neural networks with impulses. Neurocomputing 70, 2495–2501 (2007)

    Article  Google Scholar 

  27. Yang, Y., Cao, J.: Stability and periodicity in delayed cellular neural networks with impulsive effects. Nonlinear Anal. 7, 362–374 (2007)

    Google Scholar 

  28. Wang, Q., Liu, X.: Exponential stability of impulsive cellular neural networks with time delay via Lyapunov functionals. Appl. Math. Comput. 194, 86–198 (2007)

    Google Scholar 

  29. Gui, Z., Yang, X., Ge, W.: Existence and global exponential stability of periodic solutions of recurrent cellular neural networks with impulses and delays. Math. Comput. Simul. 79, 14–29 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  30. Benchohra, M., Ouahabi, A.: Some uniqueness results for impulsive semilinear neutral functional differential equations. Georgian Math. J. 9, 423–430 (2002)

    MathSciNet  MATH  Google Scholar 

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Correspondence to Xiaohu Wang.

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Wang, X., Li, S. & Xu, D. Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays. Nonlinear Dyn 64, 65–75 (2011). https://doi.org/10.1007/s11071-010-9846-8

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  • DOI: https://doi.org/10.1007/s11071-010-9846-8

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