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A Novel Analysis of Hopf Bifurcation for a Generalized Binary Fractional‐Order Neural Network Involving Mixed Delays

Author

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  • Long Li
  • Yanxia Zhang

Abstract

This paper provides an extensive binary fractional‐order neural network system with mixed delays consisting of two discrete delays and two distributed delays and emphasizes novel bifurcation methods and theoretical analysis. First, the original system is transformed into a five‐neuron fractional‐order neural network with four delays by introducing three virtual neurons. And then we select different delays as parameters inducing bifurcation to determine the ranges of guaranteeing the steady state response of the system. Some sufficient conditions for the occurrence of Hopf bifurcation are established. In the end, the correctness of the obtained conclusions is verified with the support of numerical simulations. It is found that both discrete and distributed delays play a key role in determining the Hopf bifurcation of fractional‐order neural networks, especially the mean delay in distributed term has a great impact on the critical values controlling bifurcation.

Suggested Citation

  • Long Li & Yanxia Zhang, 2025. "A Novel Analysis of Hopf Bifurcation for a Generalized Binary Fractional‐Order Neural Network Involving Mixed Delays," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:2366847
    DOI: 10.1155/jom/2366847
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    References listed on IDEAS

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    1. Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    2. Zhou, Xiaobing & Wu, Yue & Li, Yi & Yao, Xun, 2009. "Stability and Hopf bifurcation analysis on a two-neuron network with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1493-1505.
    3. Zheng, Bibo & Wang, Zhanshan, 2022. "Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 430(C).
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