Skip to main content
SpringerLink
Log in

Stability and Synchronization Analysis of Discrete-Time Delayed Neural Networks with Discontinuous Activations

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, both stability and synchronization of discrete-time delayed neural networks with discontinuous activations are investigated. By means of functional differential inclusions and Kakutani’s fixed point theorem, conditions are derived to ensure the existence and uniqueness of the solution. Besides, we obtain some novel sufficient conditions for global attractivity and asymptotic stability of the discontinuous discrete-time neural networks via the Halanay-type inequality and the comparison principle. Furthermore, under weaker conditions than Lipschitz conditions, we also select two different controllers to guarantee synchronization of the discrete-time neural networks with discontinuous activations. Finally, some examples with numerical simulation are given to demonstrate 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
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Aubin J, Cellina A (1984) Differential inclusions. Springer, Berlin

    Book  Google Scholar 

  2. Aubin J, Frankowska H (1990) Set-valued analysis. Birkauser, Boston

    MATH  Google Scholar 

  3. Filippov A (1988) Differential equations with discontinuous right-hand side. Mathematics and its applications. Kluwer Academic, Boston

    Book  Google Scholar 

  4. Li J, Dong H, Wang Z, Hou N, Alsaadi F (2017) On passivity and robust passivity for discrete-time stochastic neural networks with randomly occurring mixed time delays, pp 1–14

  5. Kennedy M, Chua L (1988) Neural networks for nonlinear program-ming. IEEE Trans Circuits Syst 35:554–562

    Article  Google Scholar 

  6. Yan J, Zhao A (1988) Oscillation and stability of linear impulsive delay differential equations. Math Anal Appl 227:187

    Article  MathSciNet  Google Scholar 

  7. Cao J (2003) New results concerning exponential stability and periodic solutions of delayed cellular neural networks with delays. Phys Lett A 307:136

    Article  MathSciNet  Google Scholar 

  8. Wan Y, Cao J, Wen G, Yu W (2016) Robust fixed-time synchronization of delayed Cohen–Grossberg neural networks. Neural Netw 73:86

    Article  Google Scholar 

  9. Ge F, Kou C (2015) Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear fractional differential equations. Appl Math Comput 257:308

    MathSciNet  MATH  Google Scholar 

  10. Zhou L, Zhang Y (2016) Global exponential stability of a class of impulsive recurrent neural networks with proportional delays via fixed point theory. J Frankl Inst 353:561

    Article  MathSciNet  Google Scholar 

  11. Zhang X, Han Q (2014) Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach. Neural Netw 54:57

    Article  Google Scholar 

  12. Xie D, Jiang Y (2016) Global exponential stability of periodic solution for delayed complex-valued neural networks with impulses. Neurocomputing 207:528

    Article  Google Scholar 

  13. Park M, Kwon O, Park J, Lee S, Cha E (2014) Synchronization of discrete-time complex dynamical networks with interval time-varying delays via non-fragile controller with randomly occurring perturbation. J Frankl Inst 351:4850–4871

    Article  MathSciNet  Google Scholar 

  14. Mohamad S, Gopalsamy K (2003) Exponential stability of continuous-time and discrete-time cellular neural networks with delays. Appl Math Comput 135:17–38

    MathSciNet  MATH  Google Scholar 

  15. Wang J, Jiang H, Hu C, Ma T (2014) Convergence behavior of delayed discrete cellular neural network without periodic coefficients. Neural Netw 53:61–68

    Article  Google Scholar 

  16. Ding S, Wang Z, Zhan H (2016) Dissipativity analysis for stochastic memristive neural networks with time-varying delays: a discrete-time case. IEEE Trans Neural Netw Learn Syst 99:1–13

    Article  Google Scholar 

  17. Mohamad S, Gopalsamy K (2000) Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math Comput Simul 53:1–39

    Article  MathSciNet  Google Scholar 

  18. Forti M, Nistri P (2003) Global convergence of neural networks with discontinuous neuron activations. IEEE Trans Circuits Syst I Regul Pap 50:1421–1435

    Article  MathSciNet  Google Scholar 

  19. Forti M, Grazzini M, Nistri P, Pancioni L (2006) Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations. Phys D 214:88–89

    Article  MathSciNet  Google Scholar 

  20. Qin S, Cheng Q, Chen G (2016) Global exponential stability of uncertain neuralnetworks with discontinuous Lurie-type activation and mixed delays. Neurocomputing 198:12–19

    Article  Google Scholar 

  21. Cai Z, Huang L (2015) New exponential synchronization criteria for time-varying delayed neural networks with discontinuous activations. Neural Netw 65:105–114

    Article  Google Scholar 

  22. Wang J, Huang L, Guo Z (2009) Dynamical behavior of delayed Hopfield neural networks with discontinuous activations. Appl Math Model 33:1793–1802

    Article  MathSciNet  Google Scholar 

  23. Cai Z, Huang L (2011) Existence and global asymptotic stability of periodic solution for discrete and distributed time-varying delayed neural networks with discontinuous activations. Neurocomputing 74:3170–3179

    Article  Google Scholar 

  24. Wang D, Huang L (2016) Periodicity and multi-periodicity of generalized Cohen–Grossberg neural networks via functional differential inclusions. Nonlinear Dyn 85:67–86

    Article  MathSciNet  Google Scholar 

  25. Bao G, Zeng Z (2016) Global asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functions. Neurocomputing 193:242–249

    Article  Google Scholar 

  26. Saravanakumar R, Rajchakit G, Ali M, Xiang Z, Joo Y (2017) Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays. Neural Comput Appl 1–12 https://doi.org/10.1007/s00521-017-2974-z

  27. Abdurahman A, Jiang H (2016) New results on exponential synchronization of memristor-based neural networks with discontinuous neuron activations. Neural Netw 84:161–171

    Article  Google Scholar 

  28. Liu X, Wang F, Tang M, Qiu S (2017) Stability and synchronization analysis of neural networks via Halanay-type inequality. J Comput Appl Math 319:14–23

    Article  MathSciNet  Google Scholar 

  29. Wang L, Wang Q (1991) Ordinary difference equation. Xinjiang University Press, Xinjiang

    Google Scholar 

  30. Mu X, Chen Y (2016) Synchronization of delayed discrete-time neural networks subject to saturated time-delay feedback. Neurocomputing 175:293–299

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editor, associate editor and the anonymous reviewers for their help comments and suggestions.

Author information

Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Ürümqi, 830046, Xinjiang, China

    Jinling Wang, Haijun Jiang & Cheng Hu

  2. Qinghai University, Xining, 810016, Qinghai, China

    Tianlong Ma

Authors
  1. Jinling Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haijun Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tianlong Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cheng Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haijun Jiang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work was supported in part by the Excellent Doctor Innovation Program of Xinjiang University under Grant XJUBSCX-2016004, in part by the National Natural Science Foundation of People’s Republic of China (Grant Nos. U1703262, 61473244, 61563048, 11402223).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, J., Jiang, H., Ma, T. et al. Stability and Synchronization Analysis of Discrete-Time Delayed Neural Networks with Discontinuous Activations. Neural Process Lett 50, 1549–1570 (2019). https://doi.org/10.1007/s11063-018-9943-0

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-018-9943-0

Keywords

Search

Navigation