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New bifurcation results for fractional BAM neural network with leakage delay

Author

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  • Huang, Chengdai
  • Meng, Yijie
  • Cao, Jinde
  • Alsaedi, Ahmed
  • Alsaadi, Fuad E.

Abstract

Recently, the dynamics of the fractional delayed neural networks has been considerably concerned. It is illustrated that time delay has a remarkable influence on the dynamical behaviors of the fractional neural networks. Nevertheless, the results of the fractional neural network with leakage delay are extremely few. It is the first time that the stability and bifurcation of fractional BAM neural networks with time delay in leakage terms is examined in the current paper. The stability criterion and the conditions of bifurcation are obtained for the proposed systems with or without leakage delay by selecting time delay as the bifurcation parameter. It is amazing that the leakage delay has a destabilizing influence on the stability performance of such system and they cannot be ignored. Moreover, the relation between the bifurcation point and the order is fully discussed by careful calculation. Finally, numerical examples are addressed to verify the feasibility of the obtained theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:100:y:2017:i:c:p:31-44
    DOI: 10.1016/j.chaos.2017.04.037
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    References listed on IDEAS

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    1. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
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    7. Xujun Yang & Qiankun Song & Yurong Liu & Zhenjiang Zhao, 2014. "Uniform Stability Analysis of Fractional-Order BAM Neural Networks with Delays in the Leakage Terms," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-16, June.
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    Cited by:

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    5. Călin-Adrian Popa & Eva Kaslik, 2020. "Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    6. Shuai Li & Chengdai Huang & Xinyu Song, 2019. "Bifurcation Based-Delay Feedback Control Strategy for a Fractional-Order Two-Prey One-Predator System," Complexity, Hindawi, vol. 2019, pages 1-13, April.
    7. 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.
    8. Chen, Jing & Xiao, Min & Wu, Xiaoqun & Wang, Zhengxin & Cao, Jinde, 2022. "Spatiotemporal dynamics on a class of (n+1)-dimensional reaction–diffusion neural networks with discrete delays and a conical structure," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    9. Liu, Xijuan & Liu, Yun & Wang, Shuguo & Yan, Huijie & Liao, Pengtai, 2019. "Bifurcation analysis of a magnetically supported rigid rotor in auxiliary bearings," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 328-336.
    10. Wang, Yangling & Cao, Jinde & Huang, Chengdai, 2022. "Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    11. Oliveira, José J., 2022. "Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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