神经元的混合模式振荡及动力学研究

发布时间：2018-06-17 06:17

本文选题：神经元 + 混合模式振荡　；参考：《华南理工大学》2016年博士论文

【摘要】：神经动力学以利用动力学原理研究神经元的电生理活动为基础,通过构建神经元模型来研究神经系统的分岔,混沌,振荡等动力学性质.本文以混合模式振荡为主要研究对象,分析神经元模型中此类现象的变化规律,并且解释其中两个模型中混合模式振荡的产生机理.同时分析神经元模型中平衡点的分支,峰峰间距序列的分岔以及峰的变化等问题,得到丰富的动力学结果.论文分为四部分：开篇第一章介绍神经元中混合模式振荡现象的研究进展.从几何奇异摄动理论入手,介绍基本概念和基本理论,并且解释混合模式振荡的产生机制,最后给出典型的具有混合模式振荡的神经元及其模型.接下来的两章重点分析神经元模型中混合模式振荡的产生机理.在第二章中,基于Av-Ron-Parnas-Segel模型,研究阂下混合模式振荡以及模型的动力学行为Av-Ron-Parnas-Segel模型是一个衡量龙虾心脏神经节的四维模型.首先利用几何奇异摄动理论中的折结点原理,分析简化后三维神经元模型中的混合模式振荡的产生机理.然后研究简化模型以及原模型中混合模式振荡的变化规律.得到动作电位峰峰间距序列的倍周期分岔图与加周期分岔图,以及发放数的阶梯状改变等结果.最后探讨神经元模型中的参数对系统的影响.利用峰峰间距分岔图,发现离子的平衡电位与最大电导都能改变系统的发放模式.在第三章中,研究模拟胰腺β-细胞生理活动的Chay-Keizer模型的高位平台簇放电与其周期解的转迁.首先利用快慢动力学分析方法将系统分为快慢两部分,以慢变量为参数分析簇发放以及混合模式振荡的产生原因.然后进行全系统的平衡点分支分析,重点给出Bogdanov-Takens分支附近的拓扑结构.最后探讨参数对模型的影响,其结果以峰峰间距序列和极值的分岔图以及双参数下单簇内峰数目变化图给出.在第四章中,研究高维神经元模型的动力学性质.第一部分研究一类七维固有簇放电类神经元的数学模型.固有簇放电类神经元是在构建丘脑-皮层回路的过程中提出的一类神经元.对于此类模型首先给出一种降维方式将方程简化成一个三维模型.然后研究三维模型中余维1分支与余维2分支,给出Bogdanov-Takens分支附近的分支行为.最后利用快慢动力学并借助相平面解释系统簇发放的成因.第二部分主要研究受外电场影响的Chay模型与神经回路的混合模式振荡.文中观察到丰富的混合模式振荡现象.
[Abstract]:Neurodynamics is based on the study of the electrophysiological activities of neurons by using the principle of dynamics, and the dynamical properties of the nervous system, such as bifurcation, chaos, oscillation and so on, are studied by constructing a neuron model. In this paper, the mixed mode oscillation is taken as the main research object, the variation law of this kind of phenomenon in the neuron model is analyzed, and the mechanism of the mixed mode oscillation in the two models is explained. At the same time, the bifurcation of the equilibrium point, the bifurcation of the peak-to-peak interval sequence and the variation of the peak in the neuronal model are analyzed, and rich dynamic results are obtained. The thesis is divided into four parts: the first chapter introduces the research progress of mixed mode oscillation in neurons. Based on the theory of geometric singularity perturbation, the basic concepts and theories are introduced, and the mechanism of mixed mode oscillation is explained. Finally, the typical neurons with mixed mode oscillation and their models are given. The next two chapters focus on the mechanism of mixed mode oscillation in the neuron model. In the second chapter, based on the Av-Ron-Parnas-Segel model, the mixed mode oscillation and the dynamic behavior of the model are studied. The Av-Ron-Parnas-Segel model is a four-dimensional model to measure the lobster cardiac ganglion. Firstly, the mechanism of mixed mode oscillation in the simplified three-dimensional neuron model is analyzed by using the folded node principle in the geometric singular perturbation theory. Then the variation law of the simplified model and the mixed mode oscillation in the original model is studied. The double period bifurcation diagram and the additive period bifurcation diagram of the peak-to-peak interval sequence of the action potential are obtained, as well as the ladder changes of the number of emitters. Finally, the influence of the parameters in the neuron model on the system is discussed. It is found that both the equilibrium potential and the maximum conductance of ions can change the distribution mode of the system by using the peak-to-peak bifurcation diagram. In Chapter 3, the Chay-Keizer model, which simulates the physiological activities of pancreatic 尾 -cells, is used to study the high platform discharge and the transition of its periodic solutions. Firstly, the system is divided into two parts by using the fast and slow dynamics analysis method. The slow variable is used as the parameter to analyze the distribution of the cluster and the cause of the mixed mode oscillation. Then the equilibrium bifurcation of the whole system is analyzed and the topological structure near Bogdanov-Takens bifurcation is given. Finally, the effect of the parameters on the model is discussed. The results are given by the bifurcation diagram of the peak-to-peak interval sequence and extreme value, and the variation diagram of the number of peaks in a single cluster under two parameters. In chapter 4, the dynamic properties of high dimensional neuron model are studied. In the first part, the mathematical model of a class of seven dimensional intrinsic cluster discharge neurons is studied. Intrinsic cluster discharge neurons are proposed in the process of constructing thalamic-cortical circuits. For this kind of model, a dimensionality reduction method is presented to simplify the equation into a three-dimensional model. Then the bifurcation behavior near Bogdanov-Takens bifurcation is given. Finally, the causes of cluster distribution are explained by using fast and slow dynamics and phase plane. In the second part, the mixed mode oscillation of Chay model and neural circuit affected by external electric field is studied. A wealth of mixed mode oscillations have been observed.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：R338

【相似文献】