Skip to main content
SpringerLink
Log in

Stability Analysis of Anti-periodic Neutral Type SICNNs with D Operator

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, a class of neutral type shunting inhibitory cellular neural networks with D operator are considered. Several novel conditions which guarantee the existence and exponential stability of anti-periodic solutions for the considered models are established by using Lyapunov functional method and differential inequality techniques. Moreover, an example and its numerical simulations are given to show the effectiveness 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. Haykin S (1994) Neural networks: a comprehensive foundation. Prentice Hall, New York

    MATH  Google Scholar 

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

    Book  Google Scholar 

  3. Cohen MA, Grossberg S (1983) Absolute stability of global pattern for- mation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybern 13:815–826

    Article  MATH  Google Scholar 

  4. Faydasicok O, Arik S (2012) Robust stability analysis of a class of neural networks with discrete time delays. Neural Netw 29–30:52–59

    Article  MATH  Google Scholar 

  5. Forti M, Tesi A (1995) New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans Circuits Syst I: Fundam Theory Appl 42:354–366

    Article  MathSciNet  MATH  Google Scholar 

  6. Liao X, Chen G, Sanchez EN (2002) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach. Neural Netw 15(7):855–866

    Article  Google Scholar 

  7. Chen Z (2013) A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput Appl 23:2429–2434

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. Zhao C, Wang Z (2015) Exponential convergence of a SICNN with leakage delays and continuously distributed delays of neutral type. Neural Process Lett 41:239–247

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. 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 

  12. Zhao C, Fan Q, Wang W (2010) Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying coefficients. Neural Process Lett 31:259–267

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Jiang A (2016) Exponential convergence for HCNNs with oscillating coefficients in leakage terms. Neural Process Lett 43:285–294

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Hale JK, Mawhin J (1975) Coincidence degree and periodic solutions of neutral equations. J Differ Equ 15:295–307

    Article  MathSciNet  MATH  Google Scholar 

  17. Komanovskii VB, Nosov VR (1986) Stability of functional differential equations. Academic Press, London

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu B, Huang L (2006) Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations. J Math Anal Appl 322(1):121–132

    Article  MathSciNet  MATH  Google Scholar 

  20. Liu B, Huang L (2007) Existence and uniqueness of periodic solutions for a kind of first order neutral functional differential equations with a deviating argument. Taiwan J Math 11(2):497–510

    Article  MathSciNet  MATH  Google Scholar 

  21. Peng L, Wang L (2014) Periodic solutions for first order neutral functional differential equations with multiple deviating arguments. Ann Pol Math 111(2):197–213

    Article  MathSciNet  MATH  Google Scholar 

  22. Yao L (2017) Global exponential convergence of neutral type shunting inhibitory cellular neural networks with D operator. Neural Process Lett 45:401–409

    Article  Google Scholar 

  23. Chen Z (2017) Global exponential stability of anti-periodic solutions for neutral type CNNs with D operator. Int J Mach Learn Cybern. doi:10.1007/s13042-016-0633-9

  24. Hale JK (1980) Ordinary differential equations. Krieger, Malabar

    MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Scientific Research Foundation of Hunan Provincial Education Department (Grant No. 17C1485), the Natural Scientific Research Foundation of Xiangnan University (Grant No. 2016XJ27), and the Science and Technology Innovation Team project of Xiangnan University (2017).

Author information

Authors and Affiliations

  1. School of Mathematics Finance, Xiangnan University, Chenzhou, 423000, Hunan, 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.

Ethics declarations

Conflict of interest

Author declares that he has no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, Y. Stability Analysis of Anti-periodic Neutral Type SICNNs with D Operator. Neural Process Lett 47, 1297–1307 (2018). https://doi.org/10.1007/s11063-017-9696-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-017-9696-1

Keywords

Mathematics Subject Classification

Search

Navigation