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Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation

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  • Xu, Changjin
  • Liu, Zixin
  • Liao, Maoxin
  • Li, Peiluan
  • Xiao, Qimei
  • Yuan, Shuai

Abstract

The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Applying Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential systems, we establish a new sufficient condition to ensure the stability and the emergence of Hopf bifurcation of the addressed fractional-order BAM neural networks with multiple delays. The research indicates that the delay has a vital effect on the stability and the appearance of Hopf bifurcation of fractional-order BAM neural networks. Computer simulations are put into effect to test the effectiveness of the theoretical findings. It is shown that when the sum of time delays crosses some critical values, the stability of networks loses and Hopf bifurcation will happen.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:471-494
    DOI: 10.1016/j.matcom.2020.11.023
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    1. 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.
    2. Aouiti, Chaouki & Ben Gharbia, Imen & Cao, Jinde & Salah M’hamdi, Mohammed & Alsaedi, Ahmed, 2018. "Existence and global exponential stability of pseudo almost periodic solution for neutral delay BAM neural networks with time-varying delay in leakage terms," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 111-127.
    3. 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).
    4. Xu, Changjin, 2018. "Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 69-90.
    5. 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).
    6. 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.
    7. 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.
    8. Huang, Chengdai & Tang, Jingyong & Niu, Yantao & Cao, Jinde, 2019. "Enhanced bifurcation results for a delayed fractional neural network with heterogeneous orders," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
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    Cited by:

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    2. Du, Wentong & Xiao, Min & Ding, Jie & Yao, Yi & Wang, Zhengxin & Yang, Xinsong, 2023. "Fractional-order PD control at Hopf bifurcation in a delayed predator–prey system with trans-species infectious diseases," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 414-438.
    3. Shafiya, M. & Nagamani, G. & Dafik, D., 2022. "Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 168-186.
    4. 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).
    5. 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).
    6. Wang, Wenlong & Lin, Xiao & Zhang, Chunrui, 2021. "Resonant bifurcation of feed-forward chains and application in image contrast enhancement," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 294-307.

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