[go: up one dir, main page]
Skip to main content
SpringerLink
Log in

Synchronization of Coupled Memristor Neural Networks with Time Delay: Positive Effects of Stochastic Delayed Impulses

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

This paper mainly investigates the positive effects of delay-dependent impulses on the synchronization of delayed memristor neural networks. Different from traditional impulsive control, the impulsive sequence in this paper is assumed to have the Markovian property, and is not always stabilizing. Based on a useful inequality, mean square synchronization criterion is derived under such a kind of impulsive effect. It can be seen that the stochastic impulses play an impulsive controller role, if they are stabilizing in an “average” sense. The validity of the theoretical results is illustrated by a numerical example.

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
$34.99 /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 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
Fig. 5

Similar content being viewed by others

Explore related subjects

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

References

  1. Liu Y, Zheng Y, Liu J, Cao J, Rutkowski L (2020) Constrained quaternion-variable convex optimization: a quaternion-valued recurrent neural network approach. IEEE Trans Neural Netw Learn Syst 31(3):1022–1035

    Article  MathSciNet  Google Scholar 

  2. Wu A, Wen S, Zeng Z (2012) Synchronization control of a class of memristor-based recurrent neural networks. Inform Sci 183:106–116

    Article  MathSciNet  Google Scholar 

  3. Rakkiyappan R, Chandrasekar A, Cao J (2015) Passivity and passification of memristor-based recurrent neural networks with additive time-varying delays. IEEE Trans Neural Netw Learn Syst 26(9):2043–2057

    Article  MathSciNet  Google Scholar 

  4. Li L, Mu G (2019) Synchronization of coupled complex-valued impulsive neural networks with time delays. Neural Process Lett 50(3):2515–2527

    Article  MathSciNet  Google Scholar 

  5. Chua L (1971) Memristor-missing circuit element. IEEE Trans Circ Theory 18(5):507–519

    Article  Google Scholar 

  6. Marco MD, Forti M, Pancioni L (2018) New conditions for global asymptotic stability of memristor neural networks. IEEE Trans Neural Netw Learn Syst 29(5):1822–1834

    Article  MathSciNet  Google Scholar 

  7. Wu A, Zeng Z (2012) Exponential stabilization of memristive neural networks with time delays. IEEE Trans Neural Netw Learn Syst 23(12):1919–1929

    Article  Google Scholar 

  8. Zhang W, Li C, Huang T, Xiao M (2015) Synchronization of neural networks with stochastic perturbation via aperiodically intermittent control. Neural Netw 71:105–111

    Article  Google Scholar 

  9. Wang Y, Lu J, Liang J, Cao J, Perc M (2019) Pinning synchronization of nonlinear coupled lure networks under hybrid impulses. IEEE Trans Circ Syst II: Express Brief 66(3):432–436

    Google Scholar 

  10. Li L, Shi X, Liang J (2019) Synchronization of impulsive coupled complex-valued neural networks with delay: the matrix measure method. Neural Netw 117:285–294

    Article  Google Scholar 

  11. He W, Xu T, Tang Y, Du W, Tian Y-C, Qian F (2020) Secure communication based on quantized synchronization of chaotic neural networks under an event-triggered strategy. IEEE Trans Neural Netw Learn Syst 31(9):3334–3345

    Article  MathSciNet  Google Scholar 

  12. Yang C, Huang L, Cai Z (2019) Fixed-time synchronization of coupled memristor-based neural networks with time-varying delays. Neural Netw 116:101–109

    Article  Google Scholar 

  13. Yang Z, Luo B, Liu D, Li Y (2020) Adaptive synchronization of delayed memristive neural networks with unknown parameters. IEEE Trans Syst Man Cybernetics-syst 50(2):539–549

    Article  Google Scholar 

  14. Li N, Zheng W (2018) Synchronization criteria for inertial memristor-based neural networks with linear coupling. Neural Netw 106:260–270

    Article  Google Scholar 

  15. Xu W, Hu G, Ho D, Feng Z (2020) Distributed secure cooperative control under denial-of-service attacks from multiple adversaries. IEEE Trans Cybern 50(8):3458–3467

    Article  Google Scholar 

  16. Xu W, Ho D, Zhong J, Chen B (2019) Event/self-triggered control for leader-following consensus over unreliable network with DoS attacks. IEEE Trans Neural Netw Learn Syst 30(10):3137–3149

    Article  MathSciNet  Google Scholar 

  17. Jiang B, Lu J, Liu Y (2020) Exponential stability of delayed systems with average-delay impulses. SIAM J Control Optim 58(6):3763–3784

    Article  MathSciNet  Google Scholar 

  18. Liu Y, Xu P, Lu J, Liang J (2016) Global stability of Clifford-valued recurrent neural networks with time delays. Nonlinear Dynam 84(2):767–777

    Article  MathSciNet  Google Scholar 

  19. Yang X, Song Q, Cao J, Lu J (2019) Synchronization of coupled Markovian reaction-diffusion neural networks with proportional delays via quantized control. IEEE Trans Neural Netw Learn Syst 3(3):951–958

    Article  MathSciNet  Google Scholar 

  20. Rakkiyappan R, Gayathri D, Velmurugan G, Cao J (2019) Exponential synchronization of inertial memristor-based neural networks with time delay using average impulsive interval approach. Neural Processing Letters

  21. Lakshmikantham V, Bainov D, Simenonv P (1989) Theory of impulsive different equations. World Scientific, Singapore

    Book  Google Scholar 

  22. Duan S, Wang H, Wang L, Huang T, Li C (2017) Impulsive effects and stability analysis on memristive neural networks with variable delays. IEEE Trans Neural Netw Learn Syst 28(2):476–481

    Article  Google Scholar 

  23. Filippov AF (1988) Differential equations with discontinuous right-hand side. Mathematics and its Applications (Soviet Series), Kluwer Academic, Dordrecht

    Book  Google Scholar 

  24. Yang Z, Xu D (2007) Stability analysis and design of Impulsive control systems with time delay. IEEE Trans Autom Control 52(8):1448–1454

    Article  MathSciNet  Google Scholar 

  25. Zhang W, Qi J, He X (2018) Input-to-state stability of impulsive inertial memristive neural networks with time-varying delayed. J Franklin Inst 355(17):8971–8988

    Article  MathSciNet  Google Scholar 

  26. Yang Z, Xu D (2005) Stability analysis of delay neural networks with impulsive effects. IEEE Trans Circ Syst II: Express Briefs 52(8):517–521

    Article  Google Scholar 

  27. Lu J, Ho D, Cao J (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46(7):1215–1221

    Article  MathSciNet  Google Scholar 

  28. Wang N, Li X, Lu J, Alsaadi F (2018) Unified synchronization criteria in an array of coupled neural networks with hybrid impulses. Neural Netw 101:25–32

    Article  Google Scholar 

  29. Liu X, Zhang K (2016) Synchronization of linear dynamical networks on time scales: pinning control via delayed impulses. Automatica 72:147–152

    Article  MathSciNet  Google Scholar 

  30. Li X, Yang X, Huang T (2019) Persistence of delayed cooperative models: Impulsive control method. Appl Math Comput 342:130–146

    MathSciNet  MATH  Google Scholar 

  31. Li X, Shen J, Rakkiyappan R (2018) Exponential synchronization of discontinuous neural networks with time-varying mixed delays via state feedback and impulsive control. Appl Math Comput 329:14–22

    MathSciNet  Google Scholar 

  32. Rakkiyappan R, Velmurugan G, Li X (2015) Complete stability analysis of complex-valued neural networks with time delays and impulses. Neural Process Lett 41:435–468

    Article  Google Scholar 

  33. Sun Y, Li L, Liu X (2020) Exponential synchronization of neural networks with time-varying delays and stochastic impulses. Neural Netw 132:342–352

    Article  Google Scholar 

  34. Tang Y, Wu X, Shi P, Qian F (2020) Input-to-state stability for nonlinear systems with stochastic impulses. Automatica 113:108766

    Article  MathSciNet  Google Scholar 

  35. Wang Z, Liu Y, Liu X, Shi Y (2010) Robust state estimation for discrete-time stochastic neural networks with probabilistic measurement delays. Neurocomputing 74(1):256–264

    Article  Google Scholar 

  36. Lu W, Chen T (2006) New approach to synchronization analysis of linearly coupled ordinary differential systems. Physica D: Nonlinear Phenomena 213(2):214–230

    Article  MathSciNet  Google Scholar 

  37. Shi P, Li F (2015) A survey on Markovian jump systems: modeling and design. Int J Control Autom Syst 13:1–16

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61503115.

Author information

Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230009, China

    Lulu Li, Yifan Sun, Mengmeng Wang & Wei Huang

Authors
  1. Lulu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yifan Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mengmeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wei Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lulu Li.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, L., Sun, Y., Wang, M. et al. Synchronization of Coupled Memristor Neural Networks with Time Delay: Positive Effects of Stochastic Delayed Impulses. Neural Process Lett 53, 4349–4364 (2021). https://doi.org/10.1007/s11063-021-10600-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10600-z

Keywords

Search

Navigation