神经放电的一类随机节律和阵发混沌节律的动力学机制研究
发布时间：2019-05-26 19:48
【摘要】：最近几十年,神经科学和非线性科学相互融合渗透,形成了新兴的神经动力学。神经系统呈现出了多种的非线性动力学行为,而在神经动力学里其电活动也起到了举足轻重的作用。神经系统通过丰富的神经放电节律来接收、传递和加工信息。周期、混沌、随机神经放电节律都是神经放电的一般基本形式,因此,识别非周期神经放电节律是混沌还是随机一直是一个重要的科学问题。 本文以非线性动力学的理论为基础,将数学,物理学与生命科学的知识相结合,搭建理论模型,运用计算机数值模拟仿真的方法,研究了一类位于加周期分岔中的貌似混沌的随机神经放电节律,经过分析揭示了此类节律所具有的确定性机制和随机性机制,还研究了阵发混沌神经簇放电与峰放电的非光滑性,通过将其与典型的Ⅰ型和Ⅴ型阵发作比较,以此揭示其自身非光滑性的特点。 第1章首先介绍了非线性科学的概念和发展以及在神经系统研究中非线性动力学的应用；其次讲述了混沌理论的研究现状与进展,还有在神经系统中关于混沌的研究,包括国内学者的研究对神经放电中混沌的发展也起到了巨大的推动作用；最后概括介绍了本文的研究内容。 第2章介绍了本文的一些基本概念与基本知识,主要有：可兴奋细胞及其类型,神经元的概念,神经元的结构和类型,神经元动作电位的概念及其产生机制,神经元放电的数学模型,时间序列分析方法,非线性动力学与生物学的对应等。 第3章在神经起步点实验中发现了一类介于周期k和周期k+1(k=1,2)节律之间非周期自发放电节律,其行为是长串的周期k簇和周期k+1簇的交替。确定性理论模型Chay模型展示出了周期k和周期k+1节律的共存行为。噪声在共存区诱发出了与实验结果类似的非周期节律,说明了该类节律是噪声引起的两类簇的跃迁。非线性预报及其回归映射揭示该节律具有确定性机制；将两类簇分别转换为0和1得到一个二进制序列,对该序列进行概率分析获得了两类簇跃迁的随机机制。这说明此节律是具有确定性结构的随机节律而不是混沌。 第4章选取了确定性Chay模型在固定参数下,采用数值仿真的方法来研究周期3阵发混沌神经簇放电和峰放电的非光滑特性。通过分别计算两种阵发混沌首次,三次回归映射的导数和平均层流相长度,利用最小二乘法进行线性拟合,并将这两种阵发混沌的标度率与光滑系统产生的Ⅰ型阵发和非光滑系统产生的V型阵发进行比较,发现其标度率介于Ⅰ型阵发与Ⅴ型阵发之间。 第5章给出了本文的结论。
[Abstract]:In recent decades, neuroscience and nonlinear science have merged and permeated each other, forming a new neurodynamics. The nervous system presents a variety of nonlinear dynamic behaviors, and its electrical activity also plays an important role in neural dynamics. The nervous system receives, transmits and processes information through rich nerve discharge rhythms. Periodic, chaotic and random neural discharge rhythms are the general basic forms of neural discharge. Therefore, it has always been an important scientific problem to identify whether aperiodic nerve discharge rhythms are chaotic or random. Based on the theory of nonlinear dynamics, this paper combines the knowledge of mathematics, physics and life science, builds a theoretical model, and uses the method of computer numerical simulation. In this paper, a class of chaotic random nerve discharge rhythms in periodic bifurcation is studied, and the deterministic mechanism and random mechanism of this kind of rhythms are revealed by analysis. The non-smoothness of burst chaotic nerve cluster discharge and peak discharge is also studied, and their non-smoothness characteristics are revealed by comparing them with typical type I and V array attacks. In chapter 1, the concept and development of nonlinear science and its application in nervous system research are introduced. Secondly, the research status and progress of chaos theory are described, and the research on chaos in nervous system, including the research of domestic scholars, has also played a great role in promoting the development of chaos in neural discharge. Finally, the research content of this paper is briefly introduced. Chapter 2 introduces some basic concepts and basic knowledge of this paper, including excitable cells and their types, the concept of neurons, the structure and types of neurons, the concept of action potentials of neurons and its generating mechanism. The mathematical model of neuron discharge, time series analysis method, the correspondence between nonlinear dynamics and biology, etc. In chapter 3, a class of aperiodic spontaneous discharge rhythms between periodic k and periodic k 1 (k 鈮，
本文编号：2485587
[Abstract]:In recent decades, neuroscience and nonlinear science have merged and permeated each other, forming a new neurodynamics. The nervous system presents a variety of nonlinear dynamic behaviors, and its electrical activity also plays an important role in neural dynamics. The nervous system receives, transmits and processes information through rich nerve discharge rhythms. Periodic, chaotic and random neural discharge rhythms are the general basic forms of neural discharge. Therefore, it has always been an important scientific problem to identify whether aperiodic nerve discharge rhythms are chaotic or random. Based on the theory of nonlinear dynamics, this paper combines the knowledge of mathematics, physics and life science, builds a theoretical model, and uses the method of computer numerical simulation. In this paper, a class of chaotic random nerve discharge rhythms in periodic bifurcation is studied, and the deterministic mechanism and random mechanism of this kind of rhythms are revealed by analysis. The non-smoothness of burst chaotic nerve cluster discharge and peak discharge is also studied, and their non-smoothness characteristics are revealed by comparing them with typical type I and V array attacks. In chapter 1, the concept and development of nonlinear science and its application in nervous system research are introduced. Secondly, the research status and progress of chaos theory are described, and the research on chaos in nervous system, including the research of domestic scholars, has also played a great role in promoting the development of chaos in neural discharge. Finally, the research content of this paper is briefly introduced. Chapter 2 introduces some basic concepts and basic knowledge of this paper, including excitable cells and their types, the concept of neurons, the structure and types of neurons, the concept of action potentials of neurons and its generating mechanism. The mathematical model of neuron discharge, time series analysis method, the correspondence between nonlinear dynamics and biology, etc. In chapter 3, a class of aperiodic spontaneous discharge rhythms between periodic k and periodic k 1 (k 鈮，
本文编号：2485587
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