Skip to main content
SpringerLink
Log in

Anti-periodic solutions for cellular neural networks with oscillating coefficients in leakage terms

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

Abstract

This paper is concerned with the anti-periodic solutions for a class of cellular neural network model with oscillating coefficients in leakage terms. By applying contraction mapping fixed point theorem and differential inequality techniques, we establish some sufficient conditions to guarantee the existence and exponential stability of anti-periodic solutions for this model, which improve and supplement existing ones. Moreover, an example and its numerical simulations are given to support the theoretical 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. Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35(10):1257–1272

    Article  MathSciNet  MATH  Google Scholar 

  2. Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template elements. In: Proceedings of the 1990 IEEE international workshop on cellular neural networks and their applications, pp 12–25

  3. 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 

  4. 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 

  5. Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325:1117–1132

    Article  MathSciNet  MATH  Google Scholar 

  6. Liu B (2009) Anti-periodic solutions for forced Rayleigh-type equations. Nonlinear Anal Real World Appl 10(5):2850–2856

    Article  MathSciNet  MATH  Google Scholar 

  7. Li Y, Huang L (2009) Anti-periodic solutions for a class of Liénard-type systems with continuously distributed delays. Nonlinear Anal. Real World Appl 10(4):2127–2132

    Article  MathSciNet  MATH  Google Scholar 

  8. Lv X, Yan P, Liu D (2010) Anti-periodic solutions for a class of nonlinear second-order Rayleigh equations with delays. Commun Nonlinear Sci Numer Simul 15(11):3593–3598

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang W, Shen J (2009) Existence of solutions for anti-periodic boundary value problems. Nonlinear Anal Theory Methods Appl 70(2):598–605

    Article  MathSciNet  MATH  Google Scholar 

  10. Fan Q, Wang W, Yi X (2009) Anti-periodic solutions for a class of nonlinear nth-order differential equations with delays. J Comput Appl Math 230(2):762–769

    Article  MathSciNet  MATH  Google Scholar 

  11. Ou C (2008) Anti-periodic solution for high-order Hopfield neural networks. Comput Math Appl 56:1838–1844

    Article  MathSciNet  MATH  Google Scholar 

  12. Shao J (2009) An anti-periodic solution for a class of recurrent neural networks. J Comput Appl Math 228:231–237

    Article  MathSciNet  MATH  Google Scholar 

  13. Xu C, Zhang Q (2015) Existence and global exponential stability of anti-periodic solutions for BAM neural networks with inertial term and delay. Neurocomputing 153(4):108–116

    Article  MathSciNet  Google Scholar 

  14. Wang W (2013) Anti-periodic solution for impulsive high-order Hopfield neural networks with time-varying delays in the leakage terms. Adv Differ Eq 2013(73):1–15

    MathSciNet  Google Scholar 

  15. Peng L, Wang W (2013) Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms. Neurocomputing 111(2):27–33

    Article  MathSciNet  Google Scholar 

  16. Peng G, Huang L (2009) Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Nonlinear Anal Real World Appl 10:2434–2440

    Article  MathSciNet  MATH  Google Scholar 

  17. Li Y, Yang L (2009) Anti-periodic solutions for Cohen--Grossberg neural networks with bounded and unbounded delays. Commun Nonlinear Sci Numer Simul 14:3134–3140

    Article  MathSciNet  MATH  Google Scholar 

  18. Gong S (2009) Anti-periodic solutions for a class of Cohen--Grossberg neural networks. Comput Math Appl 58:341–347

    Article  MathSciNet  MATH  Google Scholar 

  19. Berezansky L, Braverman E (2009) On exponential stability of a linear delay differential equation with an oscillating coefficient. Appl Math Lett 22:1833–1837

    Article  MathSciNet  MATH  Google Scholar 

  20. Jiang A (2016) Exponential Convergence for HCNNs with Oscillating Coefficients in Leakage Terms. Neural Process Lett 43:285–294

    Article  Google Scholar 

  21. Jiang A (2015) Exponential convergence for shunting inhibitory cellular neural networks with oscillating coefficients in leakage terms. Neurocomputing 165:159–162

    Article  Google Scholar 

  22. Long Z (2016) New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms. Neurocomputing 171(1):503–509

    Article  Google Scholar 

  23. Liu X (2015) Improved convergence criteria for HCNNs with delays and oscillating coefficients in leakage terms. Neural Comput Appl. doi:10.1007/s00521-015-1906-z

    Google Scholar 

  24. Liu X (2015) Exponential convergence of SICNNs with delays and oscillating coefficients in leakage terms. Neurocomputing 168:500–504

    Article  Google Scholar 

  25. Chen H, Ni D, Qin J, Li S, Yang X, Wang T, Heng PA (2015) Standard plane localization in fetal ultrasound via domain transferred deep neural networks. IEEE J Biomed Health Inform 19(5):1627–1636

    Article  Google Scholar 

  26. Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1185–1196

    Article  MathSciNet  Google Scholar 

  27. Wang XZ (2015) Uncertainty in learning from big data-editorial. J Intell Fuzzy Syst 28(5):2329–2330

    Article  Google Scholar 

  28. Wang XZ, He YL, Dong LC, Zhao HY (2011) Particle swarm optimization for determining fuzzy measures from data. Inf Sci 181(19):4230–4252

    Article  MATH  Google Scholar 

  29. He YL, Wang XZ, Huang JZX (2016) Fuzzy nonlinear regression analysis using a random weight network. Inf Sci doi:10.1016/j.ins.2016.01.037 (in press)

Download references

Acknowledgments

The author would like to thank the editor and the reviewers for their helpful comments and constructive suggestions, which were very helpful in the revision of this correspondence.

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan University of Arts and Science, Changde, 415000, Hunan, People’s Republic of China

    Qiyuan Zhou

Authors
  1. Qiyuan Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qiyuan Zhou.

Additional information

This work was supported by the Natural Scientific Research Fund of Hunan Provincial of China (Grant Nos. 2016JJ6103, 2016JJ6104), and 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

Zhou, Q. Anti-periodic solutions for cellular neural networks with oscillating coefficients in leakage terms. Int. J. Mach. Learn. & Cyber. 8, 1607–1613 (2017). https://doi.org/10.1007/s13042-016-0531-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-016-0531-1

Keywords

Search

Navigation