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

ZHANG Wen-yu, LI Ming-hui, CHENG Zun-shui

doi:10.13371/j.cnki.chin.q.j.m.2025.02.005

Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 2: 169 - 179

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.02.005

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

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School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China

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.

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.

Received date: 2024-11-02

Online published: 2025-06-30

Supported by

Supported by Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2020MF080 and ZR2020MF065).

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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

Cite this article

ZHANG Wen-yu, LI Ming-hui, CHENG Zun-shui . The Dynamic Behavior of Asymmetric Large-Scale Ring Neural Network with Multiple Delays[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(2) : 169 -179 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.005

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