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Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays

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  • Xu, Changjin
  • Liu, Zixin
  • Yao, Lingyun
  • Aouiti, Chaouki

Abstract

This study mainly explores fractional-order six-neuron bi-directional associative memory (BAM) neural networks involving multi-delays. Taking advantage of contraction mapping principle, we prove that the solution of the addressed BAM neural networks exists and is unique. Utilizing a acceptable function, we confirm that the solution of the addressed BAM neural networks is bounded. By applying a suitable variable substitution, new fractional order six-neuron BAM neural networks involving mult-delays are converted to a class of fractional order six-neuron BAM neural networks with single delay. Using the stability criterion and bifurcation theory of fractional order differential dynamical systems, we carry out a detailed discussion on the stability and the onset of Hopf bifurcation of the established BAM neural networks. The study shows that the time delay is an important factor which affects the stability behavior and Hopf bifurcation of the involved neural networks. Numerical simulation plots are presented to illustrate our derived key conclusions. The derived analytical findings of the study play a vital role in optimizing and designing neural networks.

Suggested Citation

  • Xu, Changjin & Liu, Zixin & Yao, Lingyun & Aouiti, Chaouki, 2021. "Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005476
    DOI: 10.1016/j.amc.2021.126458
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    1. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    2. Pratap, A. & Raja, R. & Cao, J. & Rihan, Fathalla A. & Seadawy, Aly R., 2020. "Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2019. "Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 868-883.
    4. Huang, Chengdai & Meng, Yijie & Cao, Jinde & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "New bifurcation results for fractional BAM neural network with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 31-44.
    5. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. 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.
    7. Syed Ali, M. & Narayanan, Govindasamy & Shekher, Vineet & Alsulami, Hamed & Saeed, Tareq, 2020. "Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms," Applied Mathematics and Computation, Elsevier, vol. 369(C).
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    Cited by:

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    8. Mo, Wenjun & Bao, Haibo, 2022. "Finite-time synchronization for fractional-order quaternion-valued coupled neural networks with saturated impulse," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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