Skip to main content
SpringerLink
Log in

Synchronization of Coupled Complex-Valued Impulsive Neural Networks with Time Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, we mainly investigate synchronization of complex-valued neural networks (CVNNs) with time delays and impulsive effects. By using Lyapunov method and some inequality techniques, some sufficient conditions for the synchronization of CVNNs with time delays and impulsive effects are proposed. Finally, a numerical example based on small-world networks is presented to demonstrate correctness of the theoretical 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
Fig. 5

Similar content being viewed by others

References

  1. Cao JD, Wan Y (2014) Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays. Neural Netw 53:165–172

    Article  Google Scholar 

  2. Li LL, Cao JD (2011) Cluster synchronization in an array of coupled stochastic delayed neural networks via pinning control. Neurocomputing 74:846–856

    Article  Google Scholar 

  3. Yuan DM, Ho DWC, Hong YG (2016) On convergence rate of distributed stochastic gradient algorithm for convex optimization with inequality constraints. SIAM J Control Optim 54(5):2872–2892

    Article  MathSciNet  Google Scholar 

  4. Lu JQ, Ding CD, Lou JG, Cao JD (2015) Outer synchronization of partially coupled dynamical networks via pinning impulsive controllers. J Frankl Inst 352:5014–5041

    MathSciNet  MATH  Google Scholar 

  5. Liu XY, Cao JD, Yu WW, Song Q (2016) Nonsmooth finite-time synchronization of switched coupled neural networks. IEEE Trans Cybern 46(10):2360–2371

    Article  Google Scholar 

  6. Yuan DM, Hong YG, Ho DWC, Jiang GP (2018) Optimal distributed stochastic mirror descent for strongly convex optimization. Automatica 90:196–203

    Article  MathSciNet  Google Scholar 

  7. Wu W, Chen TP (2009) Partial synchronization in linearly and symmetrically coupled ordinary differential systems. Phys D 238:355–364

    Article  MathSciNet  Google Scholar 

  8. Li LL, Ho DWC, Cao JD, Lu JQ (2016) Pinning cluster synchronization of an array of coupled neural networks under event-triggered mechanism. Neural Netw 76:1–12

    Article  Google Scholar 

  9. Huang C, Ho DWC, Lu JQ (2015) Partial-information-based synchronization analysis for complex dynamical networks. J Frankl Inst 352:3458–3475

    Article  MathSciNet  Google Scholar 

  10. Lu JQ, Ho DWC, Cao JD, Kurths J (2013) Single impulsive controller for globally exponential synchronization of dynamical networks. Nonlinear Anal: Real World Appl 14:581–593

    Article  MathSciNet  Google Scholar 

  11. Lu WL, Chen TP (2011) Synchronization of coupled connected neural networks with delays. IEEE Trans Circuits Syst I 51(12):2491–2503

    Article  MathSciNet  Google Scholar 

  12. Huang C, Ho DWC, Lu JQ, Kurths J (2015) Pinning synchronization in T-S fuzzy complex networks with partial and discrete-time couplings. IEEE Trans Fuzzy Syst 23(4):1274–1285

    Article  Google Scholar 

  13. Chen TP, Liu XW, Lu WL (2007) Pinning complex networks by a single controller. IEEE Trans Circuits Syst I 54(6):1317–1326

    Article  MathSciNet  Google Scholar 

  14. Huang C, Wang W, Cao JD, Lu JQ (2018) Synchronization-based passivity of partially coupled neural networks with event-triggered communication. Neurocomputing 319:134–143

    Article  Google Scholar 

  15. Lu JQ, Ho DWC, Cao JD, Kurths J (2011) Exponential synchronization of linearly coupled neural networks with impulsive disturbances. IEEE Trans Neural Netw 22(2):329–335

    Article  Google Scholar 

  16. Wang YQ, Lu JQ, Liang JL, Cao JD, Perc M (2019) Pinning synchronization of nonlinear coupled Lur’e networks under hybrid impulses. IEEE Trans Circuits Syst II: Express Briefs 66(3):432–436

    Article  Google Scholar 

  17. Yang JJ, Lu JJ, Li LL, Liu Y, Wang Z, Alsaadi FE (2019) Event-triggered control for the synchronization of Boolean control networks. Nonlinear Dyn. https://doi.org/10.1007/s11071-019-04857-2

    Article  Google Scholar 

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

    Article  Google Scholar 

  19. Hu J, Wang J (2012) Global stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Neural Netw Learn Syst 23(6):853–865

    Article  Google Scholar 

  20. Fang T, Sun JT (2007) Further investigate the stability of complex-valued recurrent neural networks with time-delays. IEEE Trans Autom Control 52(9):1680–1685

    Article  Google Scholar 

  21. Bohner M, Rao VSH, Sanyal S (2011) Global stability of complex-valued neural networks on time scales. Differ Equ Dyn Syst 19(1, 2):3–11

    Article  MathSciNet  Google Scholar 

  22. Song QK, Yan H, Zhao ZJ, Liu YR (2016) Global exponential stability of impulsive complex-valued neural networks with both asynchronous time-varying and continuously distributed delays. Neural Netw 81:1–10

    Article  Google Scholar 

  23. Gong WQ, Liang JL, Zhang CJ, Cao JD (2016) Nonlinear measure approach for the stability analysis of complex-valued neural networks. Neural Process Lett 44(2):539–554

    Article  Google Scholar 

  24. Yan MM, Qiu JL, Chen XY, Chen X, Yang CD, Zhang AC, Alsaadi F (2018) The global exponential stability of the delayed complex-valued neural networks with almost periodic coefficients and discontinuous activations. Neural Process Lett 48(1):577–601

    Article  Google Scholar 

  25. Yang XS, Cao JD, Qiu JL (2015) \(P\)th moment exponential stochastic synchronization of coupled memristor-based neural networks with mixed delays via delayed impulsive control. Neural Netw 65:80–91

    Article  Google Scholar 

  26. Li YY (2017) Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process Lett 46:59–69

    Article  Google Scholar 

  27. Lu JQ, Ho DWC, Cao JD (2010) A unified synchronization criterion for impulsive dynamical networks. Automatica 46:1215–1221

    Article  MathSciNet  Google Scholar 

  28. Lu JQ, Wang ZD, Cao JD, Ho DWC, Kurths J (2012) Pinning impulsive stabilization of nonlinearly dynamical networks with time-varying delay. Int J Bifurc Chaos 22(7):1250176

    Article  Google Scholar 

  29. Li YY, Lou J, Wang Z, Alsaadi FE (2018) Synchronization of nonlinearly coupled dynamical networks under hybrid pinning impulsive controllers. J Frankl Inst 355(14):6520–6530

    Article  Google Scholar 

  30. Horn R, Johnson C (1990) Matrix analysis. Cambridge University Press, Cambridge

    MATH  Google Scholar 

Download references

Acknowledgements

The work was jointly supported by the National Natural Science Foundation of China under Grants 61503115 and the Fundamental Research Funds for the Central Universities under Grants JZ2017HGTB0188.

Author information

Authors and Affiliations

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

    Lulu Li & Guohong Mu

Authors
  1. Lulu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guohong Mu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lulu Li.

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., Mu, G. Synchronization of Coupled Complex-Valued Impulsive Neural Networks with Time Delays. Neural Process Lett 50, 2515–2527 (2019). https://doi.org/10.1007/s11063-019-10028-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-019-10028-6

Keywords

Search

Navigation