具有电磁感应的丘脑底核–苍白球网络模型的分岔分析  

Bifurcation Analysis of a Subthalamic Nucleusg-globus Pallidus Network Model with Electromagnetic Induction

作　　者：易丹 郑艳红[1] 陈国泰 曾巧云 YI Dan;ZHENG Yanhong;CHEN Guotai;ZENG Qiaoyun(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117)

机构地区：[1]福建师范大学数学与统计学院,福州350117

出　　处：《工程数学学报》2025年第1期177-187,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11672074);福建省自然科学基金(2022J01657;2022J01192)。

摘　　要：帕金森病主要是由皮质–基底神经节回路中异常振荡引起的神经系统运动障碍的疾病,而电磁感应在神经元活动中有着重要的作用。引入磁通量,构建具有电磁感应的丘脑底核–苍白球网络模型,分析其产生Hopf分岔的动力学机制。通过分析相关的特征方程来研究模型的稳定性,得到带时滞的Hopf分岔的条件,数值模拟验证了理论分析的结果。研究发现,增大神经核团间的传递延迟可以诱导振荡。此外,双参数分岔分析表明磁通量k的增大对由传递延迟T和突触连接强度WCS引起的振荡具有一定的减缓作用。希望所得的结果能有助于理解磁通量在帕金森病发作中的作用。Parkinson's disease is a movement disorder of the nervous system caused by the abnormal oscillations in cortical-basal ganglia circuits,and electromagnetic induction plays an important role in neuronal activities.In this paper,a subthalamic nucleus-globus pallidus network model with electromagnetic induction is proposed to analyze the dynamic mechanism of the Hopf bifurcation with the help of the magnetic ux variable.By analyzing the characteristic equations and the stability of the model,the conditions for the occurrence of Hopf bifurcation with time delay are obtained,and numerical simulation veri es the results of theoretical analysis.It is revealed that increasing synaptic transmission delay can induced oscillations.In addition,two-parameter bifurcation analysis shows that the increase of average magnetic ux k has a certain elimination the system oscillation caused by synaptic transmission delay T and synaptic connection weight WCS.It is hoped that the results might have some help in understanding the role of electromagnetic induction in Parkinson's disease.

关 键 词：神经网络模型 帕金森病 电磁感应 时滞 HOPF分岔 

分 类 号：O175[理学—数学] O322[理学—基础数学]