Skip to main content
SpringerLink
Log in

Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

In this paper, a class of fuzzy cellular neural networks with multi-proportional delays is investigated. By applying contraction mapping fixed point theorem and differential inequality techniques, some sufficient conditions are established for the existence and global attractivity of a unique almost periodic solution for the model, which improve and supplement existing ones. Moreover, a numerical example is given to illustrate the feasibility and application of the obtained 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. Abdurahman A, Jiang H, Teng Z (2015) Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst. doi:10.1016/j.fss.2015.07.009

  2. Bao H (2015) Existence and exponential stability of periodic solution for BAM Fuzzy CohenCGrossberg neural networks with mixed delays. Neural Process Lett. doi:10.1007/s11063-015-9455-0

  3. Derfel GA (1982) On the behaviour of the solutions of functional and functional-differential equations with several deviating arguments. Ukr Math J 34:286–291

    Article  MATH  Google Scholar 

  4. Derfel GA (1990) Kato problem for functional-differential equations and difference Schr\(\ddot{o}\)dinger operators. Oper Theor 46:319–321

    MATH  Google Scholar 

  5. Dovrolis C, Stiliadisd D, Ramanathan P (1999) Proportional differentiated services: delay differentiation and packet scheduling. ACM Sigcomm Comput Commun Rev 29(4):109–120

    Article  Google Scholar 

  6. Fink AM (1974) Almost periodic differential equations, vol 377. Lecture Notes in MathematicsSpringer, Berlin

  7. Fox L, Mayers DF, Ockendon JR, Tayler AB (1971) On a functional-differential equation. J Inst Math Appl 8(3):271–307

    Article  MathSciNet  MATH  Google Scholar 

  8. Hale JK, Verduyn Lunel SM (1993) Introduction to functional differential equations. New York: Springer-Verlag

  9. 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  Google Scholar 

  10. 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 

  11. Liu B (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454

    Article  Google Scholar 

  12. Liu B (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256

    Article  Google Scholar 

  13. Liu B, Huang L (2005) Existence and exponential stability of almost periodic solutions for cellular neural networks with time-varying delays. Phys Lett A 341(1–4):135–144

    Article  MATH  Google Scholar 

  14. Liu B, Huang L (2008) Positive almost periodic solutions for recurrent neural networks. Nonlinear Anal Real World Appl 9:830–841

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  18. Ockendon JR, Tayler AB (1971) The dynamics of a current collection systemfor an electric locomotive. Proc R Soc A 322:447–468

    Article  Google Scholar 

  19. 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 

  20. Song X, Zhao P, Xing Z, Peng J (2015) Global asymptotic stability of CNNs with impulses and multi-proportional delays. Math Meth Appl Sci. doi:10.1002/mma.3515

  21. Wu J (2001) Introduction to neural dynamics and signal trasmission delay. Walter de Gruyter, Belin

    Book  Google Scholar 

  22. 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 

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

    Article  Google Scholar 

  24. 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

  25. 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 

  26. 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 

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

    Article  Google Scholar 

  28. 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 

  29. 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 

  30. Zhang Y, Zhou L (2012) Exponential stability of a class of cellular neural networks with multi-pantograph delays. Acta Electron Sin 40(6):1159–1163

    Google Scholar 

  31. Zheng CD, 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 

  32. Zhou L (2013) Delay-dependent exponential stability of Cellular neural networks with multi-proportional delays. Neural Process Lett 38:347–359

    Article  Google Scholar 

  33. Zhou L (2015) Novel global exponential stability criteria for hybrid BAM neural networks with proportional delays. Neurocomputing 161

  34. Zhou L, Zhang Y (2015) Global exponential stability of cellular neural networks with multi-proportional delays. Int J Biomath 8(6):1550071, 1–17

  35. Zhou L, Liu J (2013) Global asymptotic stability of a class of cellular neural networks with proportional delays. Chin J Eng Math 5(30):673–682, 99–106

Download references

Acknowledgments

The author thanks for the anonymous referees valuable opinions. The suggestions improve this paper and motivate some further works.

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, 415000, Hunan, China

    Zuda Huang

Authors
  1. Zuda Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zuda Huang.

Additional information

This work was supported by the Construction Program of the Key Discipline in Hunan University of Arts and Science—Applied Mathematics.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, Z. Almost periodic solutions for fuzzy cellular neural networks with multi-proportional delays. Int. J. Mach. Learn. & Cyber. 8, 1323–1331 (2017). https://doi.org/10.1007/s13042-016-0507-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-016-0507-1

Keywords

Mathematics Subject Classification

Search

Navigation