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Sufficient Conditions for Global Stability and Existence of Almost Automorphic Solution of a Class of RNNs

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Abstract

In this paper a class of recurrent neural networks with variable coefficients and mixed delays is considered. After introducing definitions and preliminary lemmas, we prove under convenient assumptions the existence of an almost automorphic solution of the considered model. Moreover, the global exponential stability of the almost automorphic solution is studied. In addition, two examples are also given to illustrate the theory.

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References

  1. Ammar, B., Chérif, F., Adel, M., Alimi, M.A.: Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. IEEE Trans. Neural Netw. Learn. Syst. 23(1), 109–118 (2012)

    Article  Google Scholar 

  2. Bochner, S.: A new approach to almost periodicity. Proc. Natl. Acad. Sci. USA 48, 195–205 (1962)

    Google Scholar 

  3. Bochner, S.: Continuous mappings of almost automorphic and almost periodic functions. Proc. Natl. Acad. Sci. USA 52, 907–910 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cao, J., Hang, H., Wang, J.: Global exponential stability and periodic solutions of recurrent neural networks with delays. Phys. Lett. A 298, 393–404 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cao, J.: New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys. Lett. A 307, 136–147 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. Cao, J., Chen, A., Huang, X.: Almost periodic attraction of delayed neural networks with variable coefficients. Phys. Lett. A 340, 104–120 (2005)

    Article  MATH  Google Scholar 

  7. Chérif, F.: Existence and global exponential stability of pseudo almost periodic solution for SICNNs with mixed delays. J. Appl. Math. Comput. 39, 235–251 (2012)

    Article  MathSciNet  Google Scholar 

  8. Diagana, T., Henriquez, H.R., Hernández, E.M.: Almost automorphic mild solutions to some partial neutral functional-differential equations and applications. Nonlinear Anal. Theory Methods Appl. 69, 1485–1493 (2008)

    Article  MATH  Google Scholar 

  9. N’Guérékata, G.M.: Topics in Almost Automorphy. Springer Verlag, New York (2005)

    MATH  Google Scholar 

  10. Gopalsamy, K., He, X.-Z.: Delayed-independent stability in bidirectional associative memory networks. IEEE Trans. Neural Netw. 5, 998–1002 (1994)

    Article  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. Hale, J.K.: Theory of Functions Differential Equations. Springer, New York (1977)

    Book  Google Scholar 

  13. Huang, H., Cao, J., Wang, J.: Global exponential stability and periodic solutions of recurrent cellular neural networks with delays. Phys. Lett. A 298, 393–404 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Huang, X., Cao, J., Ho, 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  MathSciNet  Google Scholar 

  15. Li, C., Liao, X.: New algebraic conditions for global exponential stability of delayed recurrent neural networks. Neurocomputing 64, 319–333 (2005)

    Article  Google Scholar 

  16. Liu, Y., wang, Z., Liu, X.: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw. 19, 667–675 (2006)

    Article  MATH  Google Scholar 

  17. Liu, B.: Almost periodic solutions for Hopfield neural networks with continuously distributed delays. Math. Comput. Simul. 73, 327–335 (2007)

    Article  MATH  Google Scholar 

  18. Qin, S., Xue, X., Wang, P.: Global exponential stability of almost periodic solution of delayed neural networks with discontinuous activations. Inf. Sci. 220, 367–378 (2013)

    Article  MathSciNet  Google Scholar 

  19. Xiang, H., Cao, J.: Almost periodic solutions of recurrent neural networks with continuously distributed delays. Nonlinear Anal. 71, 6097–6108 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhao, H.: Global stability of bidirectional associative memory neural networks with distributed delays. Phys. Lett. A 297, 182–190 (2002)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The author wish to thank the anonymous reviewers for their insightful and constructive comments, which help to enrich the content and improve the presentation of this paper.

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  1. ISSATs cité la Tafala and Laboratory of Mathematical Physic, Specials Functions and Applications, LR11ES35, Ecole Supérieure des Sciences et de Technologie de Hammam-Sousse, Université de Sousse, Sousse, Tunisia

    Farouk Chérif

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  1. Farouk Chérif
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Correspondence to Farouk Chérif.

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Chérif, F. Sufficient Conditions for Global Stability and Existence of Almost Automorphic Solution of a Class of RNNs. Differ Equ Dyn Syst 22, 191–207 (2014). https://doi.org/10.1007/s12591-013-0168-4

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