ZENG Qiaoyun,ZHENG Yanhong,YI Dan.Bifurcation analysis of abnormal oscillations in a class of Parkinson’s disease model with time delay[J].Journal of Yanbian University,2023,(03):230-235.
一类具有时滞的帕金森病模型异常振荡的分岔分析
- Title:
- Bifurcation analysis of abnormal oscillations in a class of Parkinson’s disease model with time delay
- 文章编号:
- 1004-4353(2023)03-0230-06
- Keywords:
- Parkinson’s disease model; oscillation; Hopf bifurcation; time delay; connection weight; subthalamic nucleus - globus pallidus network
- 分类号:
- O175; O322
- 文献标志码:
- A
- 摘要:
- 研究了一个拓展的具有时滞的丘脑底核-苍白球网络模型存在振荡的理论条件,并利用Routh - Hurwitz定理推导了该模型在平衡点的稳定性.数值模拟验证表明,所得的理论条件成立,且该模型产生分岔的临界点与理论的分岔点吻合度较高.当神经元集群间的传输时滞较小时,系统处于健康状态; 当时滞较大时,系统会发生过度的beta振荡,即系统会处于帕金森病状态; 神经元集群间的连接权值也可对系统的振荡产生影响.
- Abstract:
- In this paper, the theoretical conditions of oscillations in an extended subthalamic nucleus - globus pallidus network(STN - GP)model with time delay were studied.And the stability of the model at equilibrium point was deduced by Routh - Hurwitz theorem.Numerical simulation results show that the theoretical conditions are valid, and the critical points of bifurcation generated by the model are in good agreement with the theoretical bifurcation points.The system is in a healthy state when the transmission delay between neuron clusters is small.The larger time delay makes the system have excessive beta oscillation, that is, the system is in a Parkinson’s state.The connection weights between clusters of neurons can also affect the oscillation of the system.
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备注/Memo
收稿日期: 2023-05-18
基金项目: 国家自然科学基金面上项目(11672074); 福建省自然科学基金(2022J01657)
第一作者: 曾巧云(1999—),女,硕士研究生,研究方向为非线性神经动力学.
通信作者: 郑艳红(1977—),女,博士,教授,研究方向为非线性神经动力学.