Skip to main content
SpringerLink
Log in

Exponential Stability of Pseudo Almost Periodic Solutions for Fuzzy Cellular Neural Networks with Time-Varying Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper considers the exponential stability of pseudo almost periodic solutions for a class of fuzzy cellular neural networks with time-varying delays. Based on differential inequality techniques and by constructing suitable Lyapunov function, we achieve some sufficient conditions for the existence and exponential stability of pseudo almost periodic solutions for the model, which extend some previously known researches. Especially, we provide a numerical example to demonstrate the correctness of our results.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  1. Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: theory. In: Proceedings of IEEE international work shop on cellular neural networks and applications, pp 181–186

  2. Yang T, Yang L, Wu C, Chua L (1996) Fuzzy cellular neural networks: applications. In: Proceedings of IEEE international work shop on cellular neural networks and applications, pp 225–230

  3. Abdurahman A, Jiang H, Teng Z (2016) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst 297:96–111

    Article  MathSciNet  MATH  Google Scholar 

  4. Yang HZ, Sheng L (2009) Robust stability of uncertain stochastic fuzzy cellular neural networks. Neurocomputing 73:133–138

    Article  Google Scholar 

  5. Jian J, Jiang W (2015) Lagrange exponential stability for fuzzy Cohen–Grossberg neural networks with time-varying delays. Fuzzy Sets Syst 277:65–80

    Article  MathSciNet  MATH  Google Scholar 

  6. Zheng C, Zhang X, Wang Z (2015) Mode-dependent stochastic stability criteria of fuzzy Markovian jumping neural networks with mixed delays. ISA Trans 56:8–17

    Article  Google Scholar 

  7. Kao Y, Shi L, Xie J, Karimi HR (2015) Global exponential stability of delayed Markovian jump fuzzy cellular neural networks with generally incomplete transition probability. Neural Netw 63:18–30

    Article  MATH  Google Scholar 

  8. Yuan K, Cao JD, Deng JM (2006) Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays. Neurocomputing 69(13–15):1619–1627

    Article  Google Scholar 

  9. Song Q, Wang Z (2009) Dynamical behaviors of fuzzy reaction–diffusion periodic cellular neural networks with variable coefficients and delays. Appl Math Model 33:3533–3545

    Article  MathSciNet  MATH  Google Scholar 

  10. Niu S, Jiang H, Teng Z (2008) Exponential stability and periodic solutions of FCNNs with variable coefficients and time-varying delays. Neurocomputing 71:2929–2936

    Article  Google Scholar 

  11. Niu S, Jiang H, Teng Z (2009) Periodic oscillation of FCNNs with distributed delays and variable coefficients. Nonlinear Anal Real World Appl 10:1540–1554

    Article  MathSciNet  MATH  Google Scholar 

  12. Bao H (2016) EExistence and exponential stability of periodic solution for BAM fuzzy Cohen–Grossberg neural networks with mixed delays. Neural Process Lett 43(3):871–885

    Article  Google Scholar 

  13. Yang W (2014) Periodic solution for fuzzy Cohen–Grossberg BAM neural networks with both time-varying and distributed delays and variable coefficients. Neural Process Lett 40:51–73

    Article  Google Scholar 

  14. Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with time-varying delays. Neural Comput Appl 28:2313–2320

    Article  Google Scholar 

  15. Huang Z (2017) Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Int J Mach Learn Cyber 8:1323–1331

    Article  Google Scholar 

  16. Bohr HA, Cohn H (1947) Almost periodic functions. Mathematika 22(2):128–131

    Google Scholar 

  17. Zhang C (2003) Almost periodic type functions and ergodicity. Science Press, Beijing

    Book  MATH  Google Scholar 

  18. NGu érékata GM (2001) Almost automorphic functions and almost periodic functions in abstract spaces. Plenum Publishers, New York

    Book  Google Scholar 

  19. Liu B (2017) Finite-time stability of CNNs with neutral proportional delays and time-varying leakage delays. Math Methods Appl Sci 40:167–174

    Article  MathSciNet  MATH  Google Scholar 

  20. Lu W, Chen T (2005) Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A 8(48):1015–1026

    Article  MathSciNet  MATH  Google Scholar 

  21. Xu Y (2014) New results on almost periodic solutions for CNNs with time-varying leakage delays. Neural Comput Appl 25:1293–1302

    Article  Google Scholar 

  22. Zhang H, Shao J (2013) Existence and exponential stability of almost periodic solutions for CNNs with time-varying leakage delays. Neurocomputing 121(9):226–233

    Article  Google Scholar 

  23. Zhang H, Shao J (2013) Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Appl Math Comput 219(24):11471–11482

    MathSciNet  MATH  Google Scholar 

  24. Zhang H (2014) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appl 2014(24):1135–1146

    Article  Google Scholar 

  25. Liu B, Tunc C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26:429–435

    Article  Google Scholar 

  26. Zhang A (2017) Pseudo almost periodic solutions for SICNNs with oscillating leakage coefficients and complex deviating arguments. Neural Process Lett 45:183–196

    Article  Google Scholar 

  27. Zhang A (2017) Pseudo almost periodic solutions for neutral type SICNNs with D operator. J Exp Theor Artif 29(4):795–807

    Article  Google Scholar 

  28. Zhou Q, Shao J (2018) Weighted pseudo anti-periodic SICNNs with mixed delays. Neural Comput Appl. 29:865–872

    Article  Google Scholar 

  29. Xu Y (2017) Exponential stability of pseudo almost periodic solutions for neutral type cellular neural networks with D operator. Neural Process Lett 46:329–342

    Article  Google Scholar 

  30. Fink AM (1974) Almost periodic differential equations, vol 377. Lecture notes in mathematics. Springer, Berlin

    MATH  Google Scholar 

  31. Zhang C (1995) Pseudo almost periodic solutions of some differential equations II. J Math Anal Appl 192:543–561

    Article  MathSciNet  MATH  Google Scholar 

  32. Liang J. Qian H. Liu B 2017 Pseudo almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Neural Process Lett. https://doi.org/10.1007/s11063-017-9774-4

  33. Arbi A, Cao J (2017) Pseudo-almost periodic solution on time-space scales for a novel class of competitive neutral-type neural networks with mixed time-varying delays and leakage delays. Neural Process Lett 3:1–27

    Google Scholar 

  34. Arbi A (2017) Dynamics of BAM neural networks with mixed delays and leakage time-varying delays in the weighted pseudo-almost periodic on time-space scales. Math Methods Appl Sci. https://doi.org/10.1002/mma.4661

  35. Arbi A, Aouiti C, Chérif F, Touati A, Alimi AM (2015) Stability analysis for delayed high-order type of Hopfield neural networks with impulses. Neurocomputing 165(c):312–329

    Article  Google Scholar 

  36. Arbi A, Cherif C, Aouiti C, Touati A (2016) Dynamics of new class of hopfield neural networks with time-varying and distributed delays. Acta Math Sci 36(3):891–912

    Article  MathSciNet  MATH  Google Scholar 

  37. Arbi A, Alsaedi A, Cao J (2017) Delta-differentiable weighted pseudo-almost automorphicity on time-space scales for a novel class of high-order competitive neural networks with WPAA coefficients and mixed delays. Neural Process Lett 3:1–30

    Google Scholar 

  38. Arbi A, Cao J, Alsaedi A (2018) Improved synchronization analysis of competitive neural networks with time-varying delays. Nonlinear Anal Model Control 23(1):82–102

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

I would like to thank the anonymous referees and the editor for very helpful suggestions and comments which led to improvements of our original paper. This work was supported by Natural Scientific Research Fund of Hunan Provincial of China (Grant Nos. 2018JJ2372, 2018JJ2087), a Key Project Supported by Scientific Research Fund of Hunan Provincial Education Department (15A038) and Natural Scientific Research Fund of Hunan Provincial Education Department of China (Grant No. 17C1076).

Author information

Authors and Affiliations

  1. College of Mathematics and Computational Science, Hunan First Normal University, Changsha, 410205, Hunan, People’s Republic of China

    Yi Tang

Authors
  1. Yi Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yi Tang.

Ethics declarations

Conflict of interest

I confirm that we have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, Y. Exponential Stability of Pseudo Almost Periodic Solutions for Fuzzy Cellular Neural Networks with Time-Varying Delays. Neural Process Lett 49, 851–861 (2019). https://doi.org/10.1007/s11063-018-9857-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9857-x

Keywords

Mathematics Subject Classification

Search

Navigation