皮质-基底神经节-丘脑回路中皮质活动的动力学分析  

Dynamic Analysis of Cortical Activity in the Cortical-Basal Ganglia-Thalamus Circuit

作　　者：闫晨日 刘全生[1] 毕远宏 YAN Chenri;LIU Quansheng;BI Yuanhong(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;School of Statistics and Mathe matics,Inner Mongolia University of Finance and Economics,Hohhot 010070,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古财经大学统计与数学学院,呼和浩特010070

出　　处：《内蒙古大学学报（自然科学版）》2021年第2期123-128,共6页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(11702149,11562014);内蒙古自治区自然科学基金项目(2017MS0105,2017MS0108)。

摘　　要：皮质中神经元的活动与帕金森病症状密切相关。基于多巴胺调控皮质-基底神经节-丘脑回路的模型,探讨了多巴胺含量和皮质与丘脑底核间的神经元连接权重对皮质神经元活动的影响。首先,在一定的皮质与丘脑底核神经元连接权重下,做了多巴胺含量和皮质神经元活动的余维一分岔图。其次,为了更加清晰地观察这两个参数对皮质活动的影响,给出了相应的余维二分岔图,其中的分岔曲线将参数区域分为六部分,每部分的动力学由相图和时间历程图说明。文中的结果对理解皮质-基底神经节-丘脑回路中皮质神经元的活动有一定的帮助。The activity of neurons in the cortex is closely related to the symptoms of Parkinson’s disease.In this paper, based on the cortex-basal ganglia-thalamus circuit regulated by dopamine, the effects of dopamine level and the connection weight of neurons between cortex and subthalamic nucleus on the activity of cortical neurons are discussed.First, under certain weights, we have made codimension-one bifurcation diagrams of cortical activity with respect to the dopamine levels.Further, we have made condimension-two bifurcation diagram of the dopamine levels and connect weights in order to observe clearly the influence of these two parameters on the cortical activity.The bifurcation curves divide a plane of these two parameters into six parts, where the dynamics in each part is illustrated by phase diagram and time series.It is hoped that the results of this study will be helpful for understanding the activity of cortical neurons in the cortical-basal ganglia-thalamus circuit.

关 键 词：皮质活动 分岔分析 多巴胺含量 连接权重 

分 类 号：O193[理学—数学] Q332[理学—基础数学]