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Bifurcation detections of a fractional-order neural network involving three delays

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Abstract

This paper lucubrates the Hopf bifurcation of fractional-order Hopfield neural network (FOHNN) with three nonidentical delays. The type of delays in the model include leakage delay, self-connection delay and communication delay. Differentiating from traditional bifurcation exploration of delayed fractional-order system, this paper presents a succinct and systematic approach as much as possible to settle the bifurcation problem when all three delays fluctuate and aren’t convertible. In addition, this paper furnishes a humble opinion for solving bifurcation cases caused by arbitrary unequal delays. At length, we address three simulation examples to corroborate the correctness of key fruits.

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The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China under Grant No.12261009.

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Authors and Affiliations

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

    Huanan Wang, Chengdai Huang & Shuai Li

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

    Jinde Cao

  3. School of Mathematics and Physics, Guangxi Minzu University, Nanning, 530006, China

    Heng Liu

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  1. Huanan Wang
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  2. Chengdai Huang
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  4. Jinde Cao
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Correspondence to Chengdai Huang.

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Wang, H., Huang, C., Li, S. et al. Bifurcation detections of a fractional-order neural network involving three delays. J. Appl. Math. Comput. 70, 579–599 (2024). https://doi.org/10.1007/s12190-023-01972-7

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  • DOI: https://doi.org/10.1007/s12190-023-01972-7

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