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Hopf bifurcation in a fractional-order neural network with self-connection delay

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Abstract

This paper is concerned with the bifurcation problem of a two-delayed fractional-order neural network(FONN) with three neurons. To begin with, the bifurcation progresses with regard to some types of time delays are captured by employing the self-connecting delay as a bifurcation parameter. Afterwards, communication delay is viewed as a bifurcation parameter to cultivate bifurcation outcomes for the developed FONN, and the communication delay triggered-bifurcation conditions are captured. There is an evidence that FONN emanates remarkable stability as long as a smaller value of them is selected, and the stability performance deterioration and Hopf bifurcations take place once choosing a larger control time delay. Eventually, the correctness of the developed theoretical discoveries is appraised by employing numerical revelations.

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Funding

This work was jointly supported by the Youth Research Fund Project of Xinyang Normal University under [Grant No.2022-QN-044] and the Nanhu Scholars Program for Young Scholars of Xinyang Normal University [2018].

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Authors and Affiliations

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

    Chengdai Huang & Shansong Mo

  2. College of undergraduate education, Jiangxi Modern Polytechnic College, Nanchang, 330095, China

    Jie Gao

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

    Jinde Cao

  4. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

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  1. Chengdai Huang
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Correspondence to Chengdai Huang.

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Huang, C., Gao, J., Mo, S. et al. Hopf bifurcation in a fractional-order neural network with self-connection delay. Nonlinear Dyn 111, 14335–14350 (2023). https://doi.org/10.1007/s11071-023-08553-0

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