Skip to main content
SpringerLink
Log in

Discrete analogue of impulsive recurrent neural networks with both discrete and finite distributive asynchronous time-varying delays

  • Research Article
  • Published:
Cognitive Neurodynamics Aims and scope Submit manuscript

Abstract

This paper studies the dynamical characteristics of discrete analogue of impulsive recurrent neural networks with both discrete and finite distributed asynchronous time-varying delays. Firstly, the discrete impulsive system of the corresponding continuous-time model is reformed by impulsive maps and semi-discrete method. Secondly, by employing a famous delay impulsive differential inequality, several novel sufficient conditions are derived to ensure the uniqueness of equilibrium point and its global exponential stability in Lagrange sense for the discussed discrete-time impulsive system. Meanwhile, it is illustrated that the discrete-time analogue retains the uniqueness of equilibrium point of the corresponding continuous-time model, and some corollaries follow. Finally, one example is given to demonstrate the validity of our 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
Fig. 5

Similar content being viewed by others

References

  • Aouiti C, Assali E (2019) Stability analysis for a class of impulsive high-order Hopfield neural networks with leakage time-varying delays. Neural Comput Appl 31:7781–7803

    Article  Google Scholar 

  • Aouiti C, Assali E (2019) Nonlinear Lipschitz measure and adaptive control for stability and synchronization in delayed inertial Cohen-Grossberg Ctype neural networks. Int J Adapt Control Signal Process 33:1457–1477

    Article  Google Scholar 

  • Aouiti C, Dridi F (2019) New results on impulsive Cohen-Grossberg neural networks. Neural Process Lett 49:1459–1483

    Article  Google Scholar 

  • Aouiti C, Assali E, Cao J, Alsaedi A (2018) Global exponential convergence of neutral-type competitive neural networks with multi-proportional delays, distributed delays and time-varying delay in leakage delays. Int J Syst Sci 49:2202–2214

    Article  Google Scholar 

  • Aouiti C, Gharbia I, Cao J, Alsaedi A (2019) Dynamics of impulsive neutral-type BAM neural networks. J Franklin Inst 356:2294–2324

    Article  Google Scholar 

  • Aouiti C, M’hamdi M, Cherif F (2017) New results for impulsive recurrent neural networks with time-varying coefficients and mixed delays. Neural Process Lett 46:487–506

  • Beverton R, Holt S (1957) On the dynamics of exploited fish populations. Fisheries Investigations 19:1–533

    Google Scholar 

  • Bose A, Ioannou P (2003) Analysis of traffic flow with mixed manual and semiautomated vehicles. IEEE Trans Intell Transp Syst 4:173–188

    Article  Google Scholar 

  • Cao J, Song Q, Li T, Luo Q, Suna C, Zhang B (2009) Exponential stability of recurrent neural networks with time-varying discrete and distributed delays. Nonlinear Anal 10:2581–2589

    Article  Google Scholar 

  • Chen Z, Zhao D, Fu X (2009) Discrete analogue of high-order periodic Cohen-Grossberg neural networks with delay. Appl Math Comput 214:210–217

    Google Scholar 

  • Chiasson J et al (2005) The effect of time delays on the stability of load balancing algorithms for parallel computations. IEEE Trans Control Syst Technol 13:932–942

    Article  Google Scholar 

  • Feng Y, Yang X, Song Q, Cao J (2018) Synchronization of memristive neural networks with mixed delays via quantized intermittent control. Appl Math Comput 339:874–887

    Google Scholar 

  • Feng Y, Xiong X, Tang R, Yang X (2018) Exponential synchronization of inertial neural networks with mixed delays via quantized pinning control. Neurocomputing 310:165–171

    Article  Google Scholar 

  • Helbing D (2001) Traffic and related self-driven many-particle systems. Rev Modern Phys 73:1067–1141

    Article  Google Scholar 

  • Huang Z, Mohamad S, Gao F (2014) Multi-almost periodicity in semi-discretizations of a general class of neural networks. Math Comput Simul 101:43–60

    Article  Google Scholar 

  • Jia S, Chen Y (2020) Global exponential asymptotic stability of RNNs with mixed asynchronous time-varying delays. Adv Diff Equ. https://doi.org/10.1186/s13662-020-02648-3

    Article  Google Scholar 

  • Jia S, Chen Y (2021) Dynamic preservation for a class of semi-discrete recurrent neural networks. IEEE Access 9:89336–89343

    Article  Google Scholar 

  • Kaslik E, Sivasundaram S (2011) Impulsive hybrid discrete-time Hopfield neural networks with delays and multistability analysis. Neural Netw 24:370–377

    Article  PubMed  Google Scholar 

  • Li L, Chen W (2020) Exponential stability analysis of quaternion-valued neural networks with proportional delays and linear threshold neurons: continuous-time and discrete-time cases. Neurocomputing 381:152–166

    Article  Google Scholar 

  • Li L, Li C (2019) Discrete analogue for a class of impulsive Cohen-Grossberg neural networks with asynchronous time-varying delays. Neural Process Lett 49:331–345

    Article  Google Scholar 

  • Liang J, Cao J (2004) Exponential stability of continuous-time and discrete-time bidirectional associative memory networks with delays. Chaos, Solitons Fractals 22:773–785

    Article  Google Scholar 

  • Liu X, Chen T (2016) Global exponential stability for complex-valued recurrent neural networks with asynchronous time delays. IEEE Trans Neural Netwo Learn Syst 27:593–606

    Article  Google Scholar 

  • Liu X, Tang M, Martin R, Liu X (2007) Discrete-time BAM neural networks with variable delays. Phys Lett A 367:322–330

    Article  CAS  Google Scholar 

  • Ludovic M, Valerie L (2009) A note on semi-discrete modelling in the life sciences. Phil Trans R Soc A 367:4779–4799

    Article  Google Scholar 

  • 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  Google Scholar 

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

    Google Scholar 

  • Mohamad S, Gopalsamy K (2009) Exponential stability preservation in semi-discretisations of BAM networks with nonlinear impulses. Commun Nonlinear Sci Numer Simul 4:27–50

    Article  Google Scholar 

  • Onasanya B, Wen S, Feng Y, Zhang W, Xiong J (2021) Fuzzy coefficient of impulsive intensity in a nonlinear impulsive control system. Neural Process Lett. https://doi.org/10.1007/s11063-021-10614-7

    Article  Google Scholar 

  • Park J (2006) On global stability criterion for neural networks with discrete and distributed delays. Chaos, Solitons Fractals 30:897–902

    Article  Google Scholar 

  • Peng T, Qiu J, Lu J, Tu Z, Cao J (2021) Finite-time and fixed-time synchronization of quaternion-valued neural networks with/without mixed delays: an improved one-norm method. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2021.3085253

    Article  PubMed  Google Scholar 

  • 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 

  • Song Q, Cao J (2006) Stability analysis of Cohen-Grossberg neural network with both time-varying and continuously distributed delays. J Comput Appl Math 197:188–203

    Article  Google Scholar 

  • 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 

  • Song Q, Yan H, Zhao Z, Liu Y (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  PubMed  Google Scholar 

  • Sun G, Zhang Y (2014) Exponential stability of impulsive discrete-time stochastic BAM neural networks with time-varying delay. Neurocomputing 131:323–330

    Article  Google Scholar 

  • Wang Z, Liu Y, Liu X (2005) On global asymptotic stability of neural networks with discrete and distributed delays. Phys Lett A 345:299–308

    Article  CAS  Google Scholar 

  • Wang J, Jiang H, Ma T, Hu C (2018) Delay-dependent dynamical analysis of complex-valued memristive neural networks: continuous-time and discrete-time cases. Neural Netw 101:33–46

    Article  PubMed  Google Scholar 

  • Watta P, Wang K, Hassoun M (1997) Recurrent neural nets as dynamical Boolean systems with application to associative memory. IEEE Trans Neural Netw 8:1268–1280

    Article  CAS  PubMed  Google Scholar 

  • Wu S, Li C, Liao X, Duan S (2012) Exponential stability of impulsive discrete systems with time delay and applications in stochastic neural networks: A Razumikhin approach. Neurocomputing 82:29–36

    Article  Google Scholar 

  • Xia Y, Cao J, Cheng S (2007) Global exponential stability of delayed cellular neural networks with impulses. Neurocomputing 70:2495–2501

    Article  Google Scholar 

  • Xu H, Chen Y, Teo K (2010) Global exponential stability of impulsive discrete-time neural networks with time-varying delays. Appl Math Comput 217:537–544

    Google Scholar 

  • Yang F, Zhang C, Lien D, Chung L (2007) Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays. Chaos Solitons Fractals 34:1213–1219

    Article  Google Scholar 

  • Zeng Z, Huang T, Zheng W (2010) Multistability of recurrent neural networks with time-varying delays and the piecewise linear activation function. IEEE Trans Neural Netw 21:1371–1377

    Article  PubMed  Google Scholar 

  • Zhang Y, Sun J (2005) Stability of impulsive neural networks with time delays. Phys Lett A 348:44–50

    Article  CAS  Google Scholar 

  • Zhao H, Wang L, Ma C (2008) Hopf bifurcation and stability analysis on discrete-time Hopfield neural network with delay. Nonlinear Anal Real World Appl 9:103–113

    Article  Google Scholar 

  • Zhong S, Li C, Liao X (2010) Global stability of discrete-time Cohen-Grossberg neural networks with impulses. Neurocomputing 73:3132–3138

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the reviewers and editor for their constructive comments and suggestions that have improved the quality of the paper.

Author information

Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, 404020, China

    Songfang Jia & Yanheng Chen

Authors
  1. Songfang Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yanheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Songfang Jia.

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

Jia, S., Chen, Y. Discrete analogue of impulsive recurrent neural networks with both discrete and finite distributive asynchronous time-varying delays. Cogn Neurodyn 16, 733–744 (2022). https://doi.org/10.1007/s11571-021-09739-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11571-021-09739-1

Keywords

Search

Navigation