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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2025, Vol. 42 ›› Issue (1): 177-187.

• • 上一篇    下一篇

具有电磁感应的丘脑底核–苍白球网络模型的分岔分析

易  丹,  郑艳红,  陈国泰,  曾巧云   

  1. 福建师范大学数学与统计学院，福州 350117
  • 收稿日期:2022-08-07 接受日期:2023-03-20 出版日期:2025-02-15 发布日期:2025-04-15
  • 通讯作者: 郑艳红 E-mail: yaya-zyh@163.com
  • 基金资助:
    国家自然科学基金(11672074)；福建省自然科学基金(2022J01657; 2022J01192).

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

YI Dan,  ZHENG Yanhong,  CHEN Guotai,  ZENG Qiaoyun   

  1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117
  • Received:2022-08-07 Accepted:2023-03-20 Online:2025-02-15 Published:2025-04-15
  • Contact: Y. Zheng. E-mail address: yaya-zyh@163.com
  • Supported by:
    The National Natural Science Foundation of China (11672074); the Natural Science Foundation of Fujian Province (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$W_{CS}$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。

关键词: 神经网络模型, 帕金森病, 电磁感应, 时滞, Hopf分岔

Abstract:

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 flux 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 verifies 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 flux $k$ has a certain elimination the system oscillation caused by synaptic transmission delay $T$ and synaptic connection weight $W_{CS}$. It is hoped that the results might have some help in understanding the role of electromagnetic induction in Parkinson's disease.

Key words: neural network model, Parkinson's disease, electromagnetic induction, time delay, Hopf bifurcation

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