Skip to main content
SpringerLink
Log in

Exponential Stability of Weighted Pseudo Almost Periodic Solutions for HCNNs with Mixed Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper deals with a class of high-order cellular neural networks with mixed delays. By using fixed point theorem and differential inequality technique, several sufficient conditions for the existence and exponential stability of weighted pseudo almost periodic solutions for the addressed model are established. Moreover, an example with its numerical simulation is given to demonstrate the effectiveness and improvements of the proposed 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. Dembo A, Farotimi O, Kailath T (1991) High-order absolutely stable neural networks. IEEE Trans Circuits Syst 38:57–65

    Article  MATH  Google Scholar 

  2. Karayiannis NB, Venetsanopoulos AN (1995) On the training and performance of high-order neural networks. Math Biosci 129(2):143–168

    Article  MATH  Google Scholar 

  3. Chen Z, Yang M (2013) Exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Comput Appl 23:2221–2229

    Article  Google Scholar 

  4. Jia R, Yang M (2014) Convergence for HRNNs with unbounded activation functions and time-varying delays in the leakage terms. Neural Process Lett 39:69–79

    Article  Google Scholar 

  5. Yu Y, Jiao W (2014) New results on exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Process Lett 39:167–177

    Article  Google Scholar 

  6. Tunc C (2015) Pseudo almost periodic solutions for HCNNs with time-varying leakage delays. Moroc J Pure Appl Anal 1:51–69

    Article  Google Scholar 

  7. Huang Z (2016) Almost periodic solutions for fuzzy cellular neural networks with time-varying delays. Neural Comput Appl. doi:10.1007/s00521-016-2194-y

    Google Scholar 

  8. 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 

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

    Article  Google Scholar 

  10. Yu Y (2016) Exponential stability of pseudo almost periodic solutions for cellular neural networks with multi-proportional delays. Neural Process Lett. doi:10.1007/s11063-016-9516-z

    Google Scholar 

  11. 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 

  12. Zhang A (2016) Pseudo almost periodic solutions for SICNNs with oscillating leakage coefficients and complex deviating arguments. Neural Process Lett. doi:10.1007/s11063-016-9518-x

    Google Scholar 

  13. M’Hamdi M, Aouiti C, Touati A et al (2016) Weighted pseudo almost-periodic solutions of shunting inhibitory cellular neural networks with mixed delays. Acta Math Sci 36(6):1662–1682

    Article  MathSciNet  MATH  Google Scholar 

  14. Al-Islam NS, Alsulami SM, Diagana T (2012) Existence of weighted pseudo anti-periodic solutions to some non-autonomous differential equations. Appl Math Comput 218:6536–6548

    MathSciNet  MATH  Google Scholar 

  15. Diagana T (2006) Weighted pseudo almost periodic functions and applications. C R Acad Sci Paris Ser I 343(10):643–646

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu Y (2016) Weighted pseudo almost periodic delayed cellular neural networks. Neural Comput Appl. doi:10.1007/s00521-016-2820-8

    Google Scholar 

  17. Zhou Q, Shao J (2016) Weighted pseudo anti-periodic SICNNs with mixed delays. Neural Comput Appl. doi:10.1007/s00521-016-2582-3

    Google Scholar 

  18. 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 

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

    Book  Google Scholar 

Download references

Acknowledgements

Many thanks go to all reviewers, and I am feel so warm for their suggestions. Also, I would like to express the sincere appreciation to Prof. Jianli Li (Hunan Nomal University, Changsha, China) for the helpful discussion when this work was being carried out. This work was supported by the Scientific Research Foundation of Hunan Provincial Education Department (Grant No. 13A093), and the “Twelfth five-year” education scientific planning project of Hunan province (XJK014CGD084).

Author information

Authors and Affiliations

  1. School of Mathematics Finance, Xiangnan University, Chenzhou, 423000, Hunan, People’s Republic of China

    Yanli Xu

Authors
  1. Yanli Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanli Xu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, Y. Exponential Stability of Weighted Pseudo Almost Periodic Solutions for HCNNs with Mixed Delays. Neural Process Lett 46, 507–519 (2017). https://doi.org/10.1007/s11063-017-9595-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-017-9595-5

Keywords

Mathematics Subject Classification

Search

Navigation