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Influence of multiple time delays on bifurcation of fractional-order neural networks

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Listed:
  • Xu, Changjin
  • Liao, Maoxin
  • Li, Peiluan
  • Guo, Ying
  • Xiao, Qimei
  • Yuan, Shuai

Abstract

In this article, on the basis of predecessors, works, we will propose a new fractional-order neural network model with multiple delays. Letting two different delays be bifurcation parameters and analyzing the corresponding characteristic equations of considered model, we will establish a set of new sufficient criteria to guarantee the stability and the appearance of Hopf bifurcation of fractional-order network model with multiple delays. The impact of two different delays on the stability behavior and the emergence of Hopf bifurcation of involved network model is revealed. The influence of the fractional order on the stability and Hopf bifurcation of involved model is also displayed. To check the correctness of analytical results, we perform programmer simulations with software. A conclusion is drawn in the end. The analysis results in this article are innovative and have important theoretical significance in designing neural networks.

Suggested Citation

  • Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:565-582
    DOI: 10.1016/j.amc.2019.05.057
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    References listed on IDEAS

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    Cited by:

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    5. Xu, Changjin & Liu, Zixin & Liao, Maoxin & Li, Peiluan & Xiao, Qimei & Yuan, Shuai, 2021. "Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 471-494.
    6. Syed Ali, M. & Narayanan, G. & Saroha, Sumit & Priya, Bandana & Thakur, Ganesh Kumar, 2021. "Finite-time stability analysis of fractional-order memristive fuzzy cellular neural networks with time delay and leakage term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 468-485.
    7. Ma, Xindong & Yu, Yue & Wang, Lifeng, 2021. "Complex mixed-mode vibration types triggered by the pitchfork bifurcation delay in a driven van der Pol-Duffing oscillator," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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    9. Lee, S.H. & Park, M.J. & Kwon, O.M. & Choi, S.G., 2022. "Less conservative stability criteria for general neural networks through novel delay-dependent functional," Applied Mathematics and Computation, Elsevier, vol. 420(C).

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