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Bifurcations Induced by Self-connection Delay in High-Order Fractional Neural Networks

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Abstract

This paper discusses the problem of bifurcations for a delayed fractional-order neural networks (FONNs) with multiple neurons. Self-connection delay is carefully viewed as a bifurcation parameter, stability zones and bifurcation conditions are nicely established, respectively. It declares that self-connection delay immensely affects the stability and bifurcation of the developed FONNs. The explored FONNs illustrate preferable stability performance if selecting a lesser self-connection delay, and Hopf bifurcation generates once they overstep the critical values. Moreover, the effects of fractional order on the bifurcation points are fully studied. It detects that the emergence of bifurcation can be lagged as fractional order amplifies. The verification of the feasibility of the developed theory is implemented via numerical experiments.

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Acknowledgements

This work was jointly supported by the Key Scientific Research Project for Colleges and Universities of Henan Province under Grant No.20A110004 and the Nanhu Scholars Program for Young Scholars of Xinyang Normal University.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China

    Chengdai Huang

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. Yonsei Frontier Lab, Yonsei University, Seoul, Korea

    Jinde Cao

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  1. Chengdai Huang
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  2. Jinde Cao
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Correspondence to Chengdai Huang.

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Huang, C., Cao, J. Bifurcations Induced by Self-connection Delay in High-Order Fractional Neural Networks. Neural Process Lett 53, 637–651 (2021). https://doi.org/10.1007/s11063-020-10395-5

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