[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Global Mean Square Exponential Stability of Impulsive Non-autonomous Stochastic Neural Networks with Mixed Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this work, we consider a class of impulsive non-autonomous stochastic neural networks with mixed delays. By establishing a new generalized Halanay inequality with impulses, we obtain some sufficient conditions ensuring global mean square exponential stability of the addressed neural networks. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. An example is given to illustrate 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

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Liao X, Wong K, Li C (2004) Global exponential stability for a class of generalized neural networks with distributed delays, Nonlinear Anal. Real World Appl 5:527–547

    Article  MathSciNet  MATH  Google Scholar 

  2. Liao X, Wang J, Zeng Z (2005) Global asymptotic stability and global exponential stability of delayed cellular neural networks. IEEE Trans Circ Syst II 52(7):403–409

    Article  Google Scholar 

  3. Zhao H (2004) Global asymptotic stability of Hopfield neural network involving distributed delays. Neural Netw 17:47–53

    Article  MATH  Google Scholar 

  4. Chen A, Cao J, Huang L (2005) Global robust stability of interval cellular neural networks with time-varying delays. Chao Solit Fractal 23:787–799

    Article  MathSciNet  MATH  Google Scholar 

  5. Liu Y, Wang Z, Liu X (2006) Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Netw 19:667–675

    Article  MATH  Google Scholar 

  6. Wang B, Jian J, Jiang M (2010) Stability in Lagrange sense for Cohen-Grossberg neural networks with time-varying delays and finite distributed delays. Nonlinear Anal Hybrid Syst 4:65–78

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang G, Shen Y (2015) Novel conditions on exponential stability of a class of delayed neural networks with state-dependent switching. Neural Netw 71:55–61

    Article  Google Scholar 

  8. Zhang G, Shen Y, Sun J (2012) Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays. Neurocomputing 97:149–154

    Article  Google Scholar 

  9. Huang Z, Feng C, Mohamad S (2012) Multistability analysis for a general class of delayed Cohen-Grossberg neural networks. Inf Sci 187:233–244

    Article  MathSciNet  MATH  Google Scholar 

  10. Wu A, Zeng Z (2014) New global exponential stability results for a memristive neural system with time-varying delays. Neurocomputing 144:553–559

    Article  Google Scholar 

  11. Sun J, Chen J (2013) Stability analysis of static recurrent neural networks with interval time-varying delay. Appl Math Comput 221:111–120

    MathSciNet  MATH  Google Scholar 

  12. Bai Y, Chen J (2013) New stability criteria for recurrent neural networks with interval time-varying delay. Neurocomputing 121:179–184

    Article  Google Scholar 

  13. Xu L, Xu D (2008) Exponential stability of nonlinear impulsive neutral integro-differential equations. Nonlinear Anal TMA 69:2910–2923

    Article  MathSciNet  MATH  Google Scholar 

  14. Xu D, Zhu W, Long S (2006) Global exponential stability of impulsive integro-differential equation. Nonlinear Anal 64:2805–2816

    Article  MathSciNet  MATH  Google Scholar 

  15. Long S, Xu D, Zhu W (2007) Global exponential stability of impulsive dynamical systems with distributed delays. Electron J Qual Theory Differ Equ 10:1–13

    Article  MathSciNet  MATH  Google Scholar 

  16. Li X, Chen Z (2009) Stability properties for Hopfield neural networks with delays and impulsive perturbations. Nonlinear Anal Real World Appl 10:3253–3265

    Article  MathSciNet  MATH  Google Scholar 

  17. Yang X (2009) Existence and global exponential stability of periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks with delays and impulses. Neurocomputing 72:2219–2226

    Article  Google Scholar 

  18. Li X (2009) Existence and global exponential stability of periodic solution for impulsive Cohen-Grossberg-type BAM neural networks with continuously distributed delays. Appl Math Comput 215:292–307

    MathSciNet  MATH  Google Scholar 

  19. Haykin S (1994) Neural networks. Prentice-Hall, New Jersey, NJ

    MATH  Google Scholar 

  20. Gan Q, Xu R, Yang P (2010) Stability analysis of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms. Neural Process Lett 32:45–57

    Article  Google Scholar 

  21. Gan Q, Xu R (2010) Global robust exponential stability of uncertain neutral high-order stochastic hopfield neural networks with time-varying delays. Neural Process Lett 32:83–96

    Article  Google Scholar 

  22. Tang Y, Gao H, Zhang W, Kurths J (2015) Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses. Automatica 53:346–354

    Article  MathSciNet  Google Scholar 

  23. Zhang W, Tang Y, Wu X, Fang J (2014) Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans Circuits Syst I: Regul Pap 61:1220–1228

    Article  Google Scholar 

  24. Wong W, Zhang W, Tang Y, Wu X (2013) Stochastic synchronization of complex networks with mixed impulses. IEEE Trans Circuits Syst I: Regul Pap 60:2657–2667

    Article  MathSciNet  Google Scholar 

  25. Li X (2010) Existence and global exponential stability of periodic solution for delayed neural networks with impulsive and stochastic effects. Neurocomputing 73:749–758

    Article  Google Scholar 

  26. Song Q, Wang Z (2008) Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. Physica A 387:3314–3326

    Article  Google Scholar 

  27. Wang X, Guo Q, Xu D (2009) Exponential p-stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays. Math Comput Simul 79:1698–1710

    Article  MathSciNet  MATH  Google Scholar 

  28. Gui Z, Ge W (2007) Periodic solutions of nonautonomous cellular neural networks with impulses. Chaos Solitons Fractals 32:1760–1771

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhang Q, Wei X, Xu J (2008) Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays. Chaos Solitons Fractals 36:985–990

    Article  MathSciNet  MATH  Google Scholar 

  30. Zhang Q, Wei X, Xu J (2009) Exponential stability for nonautonomous neural networks with variable delays. Chaos Solitons Fractals 39:1152–1157

    Article  MathSciNet  MATH  Google Scholar 

  31. Jiang M, Shen Y (2008) Stability of nonautonomous bidirectional associative memory neural networks with delay. Neurocomputing 71:863–874

    Article  Google Scholar 

  32. Zhao H, Mao Z (2009) Boundedness and stability of nonautonomous cellular neural networks with reaction-diffusion terms. Math Comput Simul 79:1603–1617

    Article  MathSciNet  MATH  Google Scholar 

  33. Lou X, Cui B (2007) Boundedness and exponential stability for nonautonomous cellular neural networks with reaction-diffusion terms. Chaos Solitons Fractals 33:653–662

    Article  MathSciNet  MATH  Google Scholar 

  34. Niu S, Jiang H, Teng Z (2010) Boundedness and exponential stability for nonautonomous FCNNs with distributed delays and reaction-diffusion terms. Neurocomputing 73:2913–2919

    Article  Google Scholar 

  35. Long S, Li H, Zhang Y (2015) Dynamic behavior of nonautonomous cellular neural networks with time-varying delays. Neurocomputing 168:846–852

    Article  Google Scholar 

  36. Xu D, Li B, Long S, Teng L (2014) Moment estimate and existence for solutions of stochastic functional differential equations. Nonlinear Anal 108:128–143

    Article  MathSciNet  MATH  Google Scholar 

  37. Mao X (1997) Stochastic differential equations and applications. Horwood, Chichester

    MATH  Google Scholar 

  38. Song Y, Baker C (2004) Qualitative behaviour of numerical approximations to Volterra integro-differential equations. J Comput Appl Math 172:101–115

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The work is supported by National Natural Science Foundation of China under Grants 11271270, 11326118, 11501065 and 11201320, Fundamental Research Funds for the Central Universities under Grant 2682015CX059 and Natural Science Foundation of Chongqing under Grant cstc2015jcyjA00033.

Author information

Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Dingshi Li

  2. College of Science, Chongqing Jiaotong University, Chongqing, 400074, China

    Bing Li

Authors
  1. Dingshi Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bing Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dingshi Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, D., Li, B. Global Mean Square Exponential Stability of Impulsive Non-autonomous Stochastic Neural Networks with Mixed Delays. Neural Process Lett 44, 751–764 (2016). https://doi.org/10.1007/s11063-015-9492-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-015-9492-8

Keywords

Search

Navigation