数学季刊 ›› 2025, Vol. 40 ›› Issue (2): 169-179.doi: 10.13371/j.cnki.chin.q.j.m.2025.02.005

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具有多时滞的非对称大规模环形神经网络的动态行为

  

  1. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
  • 收稿日期:2024-11-02 出版日期:2025-06-30 发布日期:2025-06-30
  • 作者简介:ZHANG Wen-yu (1999-), female, native of Xi’an, Shaanxi, postgraduate of Qingdao University of Science and Technology, engages in complex networks and nonlinear dynamical systems; LI Ming-hui (2000-), female, native of Dezhou, Shandong, postgraduate of Qingdao University of Science and Technology, engages in complex networks and nonlinear dynamical systems; CHENG Zun-shui (1972-), male, native of Qingdao, Shandong, professor of Qingdao University of Science and Technology, Master supervisor, Ph.D, engages in the dynamics and control problems of complex network systems, multi-agent systems, and discrete sliding mode systems.
  • 基金资助:
    Supported by Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2020MF080 and ZR2020MF065).

The Dynamic Behavior of Asymmetric Large-Scale Ring Neural Network with Multiple Delays

  1. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
  • Received:2024-11-02 Online:2025-06-30 Published:2025-06-30
  • About author:ZHANG Wen-yu (1999-), female, native of Xi’an, Shaanxi, postgraduate of Qingdao University of Science and Technology, engages in complex networks and nonlinear dynamical systems; LI Ming-hui (2000-), female, native of Dezhou, Shandong, postgraduate of Qingdao University of Science and Technology, engages in complex networks and nonlinear dynamical systems; CHENG Zun-shui (1972-), male, native of Qingdao, Shandong, professor of Qingdao University of Science and Technology, Master supervisor, Ph.D, engages in the dynamics and control problems of complex network systems, multi-agent systems, and discrete sliding mode systems.
  • Supported by:
    Supported by Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2020MF080 and ZR2020MF065).

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摘要： The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated. The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated. Time delay is selected as the bifurcation parameter, and sufficient conditions for stability and Hopf bifurcation are derived. It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model. Furthermore, a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented. Finally, the effectiveness of the theory is verified through simulation results.

关键词: Large-scale neural network, Asymmetric ring, Coates’ flow graph method, Bifurcation, Delay

Abstract: The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated. The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated. Time delay is selected as the bifurcation parameter, and sufficient conditions for stability and Hopf bifurcation are derived. It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model. Furthermore, a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented. Finally, the effectiveness of the theory is verified through simulation results.

Key words: Large-scale neural network, Asymmetric ring, Coates’ flow graph method; Bifurcation, Delay

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