具有时滞反馈控制的分数阶HR神经元模型的动力学分析  

DYNAMICS ANALYSIS FOR THE FRACTIONAL-ORDER HINDMARSH-ROSE NEURONAL MODEL WITH TIME-DELAY FEEDBACK CONTROL

作　　者：王添 王海侠[1] WANG Tian;WANG Hai-xia(College of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing 210094,China)

机构地区：[1]南京理工大学数学与统计学院,南京210094

出　　处：《数学杂志》2023年第5期377-388,共12页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(12272062)。

摘　　要：本文研究了具有时滞反馈控制的分数阶Hindmarsh-Rose(HR)神经元模型的动力学性质.利用稳定性理论和分岔分析方法,详细研究了分数阶阶数和时滞对系统平衡点稳定性、分岔和放电行为的影响.同时获得了在分数阶模型中产生Hopf分岔的解析条件,推广了具有时滞反馈控制的整数阶HR神经元模型的相关结果.In this paper,we study the dynamics of the fractional-order Hindmarsh-Rose(HR)neuronal model with time-delay feedback control.Using stability theory and bifurcation analysis method,the e ects of fractional order and time-delay on equilibrium stability,bifurcation and dis-charge behavior are investigated in detail.At the same time,the analytical conditions for Hopf bifurcation in fractional-order model are obtained,and the relevant results of the integer-order HR neuronal model with time-delay feedback control are extended.

关 键 词：分数阶 HOPF分岔 时滞反馈控制 稳定性 HR神经元模型 

分 类 号：O175.1[理学—数学] O193[理学—基础数学]