Stability and Hopf Bifurcation Analysis of an (n+m)-Neuron Double-Ring Neural Network Model with Multiple Time Delays  

作　　者：XING Ruitao XIAO Min ZHANG Yuezhong QIU Jianlong 

机构地区：[1]College of Automation and College of Artificial Intelligence,Nanjing University of Posts and Telecommunications,Nanjing 210003,China [2]School of Automation and Electrical Engineering,Linyi University,Linyi 276000,China

出　　处：《Journal of Systems Science & Complexity》2022年第1期159-178,共20页系统科学与复杂性学报（英文版）

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.61573194,62073172,61877033;the Natural Science Foundation of Jiangsu Province of China under Grant No.BK20181389。

摘　　要：Up till the present moment,researchers have always featured the single-ring neural network.These investigations,however,disregard the link between rings in neural networks.This paper highlights a high-dimensional double-ring neural network model with multiple time delays.The neural network has two rings of a shared node,where one ring has n neurons and the other has m+1 neurons.By utilizing the sum of time delays as the bifurcation parameter,the method of Coates’flow graph is applied to obtain the relevant characteristic equation.The stability of the neural network model with bicyclic structure is discussed by dissecting the characteristic equation,and the critical value of Hopf bifurcation is derived.The effect of the sum of time delays and the number of neurons on the stability of the model is extrapolated.The validity of the theory can be verified by numerical simulations.

关 键 词：Coates’flow graph HIGH-DIMENSIONAL Hopf bifurcation STABILITY 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]