Skip to main content
Log in

Pseudo Almost Automorphic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, existence, uniqueness and global exponential stability of pseudo almost automorphic solutions for a class of recurrent neural networks with time-varying coefficients and mixed delays are established by employing the fixed point theorem and differential inequality. Numerical example with graphical illustration is given to illuminate our main results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Chérif F (2014) Sufficient conditions for global stability and existence of almost automorphic solution of a class of RNNs. Differ Equ Dyn Syst 22(2):191–207

    Article  MathSciNet  MATH  Google Scholar 

  2. Cao J, Liang J, Lam J (2004) Exponential stability of high-order bidirectional associative memory neural networks with time delays. Phys D 199:425–436

    Article  MathSciNet  MATH  Google Scholar 

  3. Abbas S, Mahto L, Hafayed M, Alimi AM (2014) Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients. Neurocomputing 142(22):326–334

    Article  Google Scholar 

  4. Ammar B, Chérif F, Alimi AM (2012) Existence and uniqueness of pseudo almost-periodic solution recurrent neural networks with time varying coefficient and mixed delays. IEEE Trans Neural Netw Learn Syst 23:109–118

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Bai C (2009) Existence and stability of almost periodic solutions of hopfield neural networks with continuously distributed delays. Nonlinear Anal 71:5850–5859

    Article  MathSciNet  MATH  Google Scholar 

  7. Liang J, Zhang J, Xiao T-J (2008) Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J Math Anal Appl 340:1493–1499

    Article  MathSciNet  MATH  Google Scholar 

  8. Xiao T-J, Liang J, Zhang J (2008) Pseudo almost automorphic solutions to semilinear differential equations in banach spaces. Semigroup Forum 76(3):518524

    Article  MathSciNet  Google Scholar 

  9. Bochner S (1964) Continuous mappings of almost automorphic and almost periodic functions. Proc Natl Acad Sci USA 52:907910

    Article  MathSciNet  Google Scholar 

  10. Zhang CY (1994) Pseudo-almost-periodic solutions of some differential equations. J Math Anal Appl 151:6276

    MathSciNet  Google Scholar 

  11. Zhang CY (1994) Integration of vector-valued pseudo-almost periodic functions. Proc Am Math Soc 121:167174

    Article  MathSciNet  Google Scholar 

  12. Abbas S, Xia Y (2015) Almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument. Neural Process Lett 42:691–702

    Article  Google Scholar 

  13. Hopfield JJ (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci USA 81:3088–3092

    Article  Google Scholar 

  14. Abbas S (2011) Pseudo almost automorphic solutions of some nonlinear integro-differential equations. Comput Math Appl 62:2259–2272

    Article  MathSciNet  MATH  Google Scholar 

  15. Ezzinbi K, Fatajou S, N’guérékata GM (2009) Pseudo-almost-automorphic solutions to some neutral partial functional differential equations in Banach spaces. Nonlinear Anal 70(4):1641–1647

    Article  MathSciNet  MATH  Google Scholar 

  16. Alia M, Ezzinbi K, Fatajou S (2009) Exponential dichotomy and pseudo-almost automorphy for partial neutral functional differential equations. Nonlinear Anal 71:2210–2226

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang Yan, Li Yong (2011) Alternative theorems for pseudo almost automorphic problems. Taiwan J Math 15(1):59–74

    MathSciNet  MATH  Google Scholar 

  18. Bai C (2008) Global stability of almost periodic solution of hopfield neural networks with neutral time-varying delays. Appl Math Comput 203:72–79

    MathSciNet  MATH  Google Scholar 

  19. Liang J, Zhang J, Xiao T-J (2008) Composition of pseudo almost automorphic and asymptotically almost automorphic functions. J Math Anal Appl 340:1493–1499

    Article  MathSciNet  MATH  Google Scholar 

  20. N’Guerekata GM (2005) Topics in almost automorphy. Springer, New York MR2107829 (2005h:34153)

    MATH  Google Scholar 

  21. Liang J, N’guérékata GM, Xiao T-J, Zhang J (2009) Some properties of pseudo-almost automorphic functions and applications to abstract differential equations. Nonlinear Anal 70:2731–2735

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chaouki Aouiti.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aouiti, C., M’hamdi, M.S. & Touati, A. Pseudo Almost Automorphic Solutions of Recurrent Neural Networks with Time-Varying Coefficients and Mixed Delays. Neural Process Lett 45, 121–140 (2017). https://doi.org/10.1007/s11063-016-9515-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-016-9515-0

Keywords

Mathematics Subject Classification

Navigation