一类多节点耦合的双环神经网络局部稳定性与Hopf分支  

Local Stability and Hopf Bifurcation of a Class of Multi-node Coupled Double-ring Neural Networks

作　　者：李俊 刘易成[1] LI Jun;LIU Yicheng(College of Science,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学理学院,湖南长沙410073

出　　处：《应用数学》2025年第2期412-423,共12页Mathematica Applicata

基　　金：湖南省自然科学青年基金(2022JJ40540);湖南省研究生创新基金(CX20230001)。

摘　　要：本文主要研究一类多节点耦合的双环神经网络的局部稳定性与Hopf分支性质.首先通过分析特征方程根的分布情况研究了时滞系统局部稳定性与Hopf分支出现的充分条件,然后利用中心流形理论和正规型方法计算得到了判定Hopf分支性质的关键参数,给出Hopf分支具体性质的充分条件,最后通过数值仿真验证理论的正确性,并讨论了环间耦合权重对稳定性与分支性质的影响.In this paper,the local stability and Hopf bifurcation properties of a class of multi-node coupled double-ring neural networks are studied.Firstly,sufficient conditions for the local stability of timedelay systems and the emergence of the Hopf bifurcation are studied by analyzing the distribution of roots of the characteristic equation.Then,key parameters for determining Hopf bifurcation are obtained by using the central manifold theory and the normal form method.And sufficient conditions for determining the specific properties of the Hopf bifurcation are also provided.Finally,the accuracy of the theory is confirmed through numerical simulation.The impact of interring coupling weights on stability and bifurcations is also discussed.

关 键 词：局部稳定性 HOPF分支 时滞 多节点耦合 

分 类 号：O175[理学—数学]