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

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  • 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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    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.
    2. Deshpande, Amey S. & Daftardar-Gejji, Varsha & Sukale, Yogita V., 2017. "On Hopf bifurcation in fractional dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 189-198.
    3. Huang, Chengdai, 2018. "Multiple scales scheme for bifurcation in a delayed extended van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 643-652.
    4. Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    5. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    6. Zhang, Jun & Wang, JinRong, 2018. "Numerical analysis for Navier–Stokes equations with time fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 481-489.
    7. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
    8. Liu, Shuxin & Yu, Yongguang & Zhang, Shuo & Zhang, Yuting, 2018. "Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 845-854.
    9. 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.
    10. Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.
    11. Wang, Jing & Ru, Tingting & Xia, Jianwei & Wei, Yunliang & Wang, Zhen, 2019. "Finite-time synchronization for complex dynamic networks with semi-Markov switching topologies: An H∞ event-triggered control scheme," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 235-251.
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    Cited by:

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    2. Yao, Wei & Wang, Chunhua & Sun, Yichuang & Zhou, Chao & Lin, Hairong, 2020. "Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    3. 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.
    4. 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.
    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. 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).
    7. 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.
    8. 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).
    9. Hu Zhang & Anwar Zeb & Aying Wan & Zizhen Zhang, 2022. "Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays," Mathematics, MDPI, vol. 10(9), pages 1-21, May.

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