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Hopf Bifurcation Of A Fractional Tri-Neuron Network With Different Orders And Leakage Delay

Author

Listed:
  • YANGLING WANG

    (School of Information Engineering, Nanjing Xiaozhuang University, Nanjing 211171, P. R. China)

  • JINDE CAO

    (School of Mathematics, Southeast University, Nanjing 210096, P. R. China3Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea)

  • CHENGDAI HUANG

    (School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China)

Abstract

This paper focuses on the Hopf bifurcation of a fractional tri-neuron network with both leakage delay and communication delay under different fractional orders. By applying fractional Laplace transform, the stability theorem of linear autonomous system and Hopf bifurcation theorem, we obtain a class of asymptotic stability criterion of zero solution as well as delay-induced Hopf bifurcation conditions for the considered system. Simultaneously, the stability and Hopf bifurcation for tri-neuron network with single fractional order are also discussed as a special case of our proposed neural network model. Finally, a simulation example is given to illustrate the efficiency of the presented theoretical results in this paper.

Suggested Citation

  • Yangling Wang & Jinde Cao & Chengdai Huang, 2022. "Hopf Bifurcation Of A Fractional Tri-Neuron Network With Different Orders And Leakage Delay," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(03), pages 1-14, May.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:03:n:s0218348x22500451
    DOI: 10.1142/S0218348X22500451
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    Cited by:

    1. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2024. "Bifurcations of a fractional three-layer neural network with different delays: Delay-dependent and order-dependent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 633(C).

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