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Delay-dependent bifurcation conditions in a fractional-order inertial BAM neural network

Author

Listed:
  • Huang, Chengdai
  • Wang, Huanan
  • Cao, Jinde
  • Liu, Heng

Abstract

This paper explores the stability and bifurcation of a Caputo fractional-order BAM neural network with time delay and inertia terms. Subsequently, the limitation in bifurcation characteristics of Caputo fractional-order delayed inertial BAM neural network (CFODIBAMNN) is surpassed. By analyzing the stability of the system without time delay, the direct method is applied that involves solving the eigenvalues to determine its stability. Ulteriorly, analyzing the system in the presence of time delays and choosing the time delay as the bifurcation parameter to identify the Hopf bifurcation properties of the system. Eventually, during the verifications, the critical values of bifurcation are accurately calculated, the fluctuation and phase diagrams for the ranges of different fractional order are simulated and the impact of fractional orders on system stability is analyzed.

Suggested Citation

  • Huang, Chengdai & Wang, Huanan & Cao, Jinde & Liu, Heng, 2024. "Delay-dependent bifurcation conditions in a fractional-order inertial BAM neural network," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924006581
    DOI: 10.1016/j.chaos.2024.115106
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    References listed on IDEAS

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    1. Chen, Yun & Li, Yaqi & Chen, Gang, 2024. "New results on stability analysis for a class of generalized delayed neural networks," Applied Mathematics and Computation, Elsevier, vol. 469(C).
    2. Wang, Huanan & Huang, Chengdai & Liu, Heng & Cao, Jinde, 2023. "Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer’s rule," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. Hou, Hu–Shuang & Zhang, Hua, 2023. "Stability and hopf bifurcation of fractional complex–valued BAM neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    4. Peng, Qiu & Jian, Jigui, 2023. "Synchronization analysis of fractional-order inertial-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 62-77.
    5. Brenden M. Lake & Marco Baroni, 2023. "Human-like systematic generalization through a meta-learning neural network," Nature, Nature, vol. 623(7985), pages 115-121, November.
    6. Chengdai Huang & Heng Liu & Yuefen Chen & Xiaoping Chen & Fang Song, 2021. "Dynamics Of A Fractional-Order Bam Neural Network With Leakage Delay And Communication Delay," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-14, May.
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