【摘要】：最近幾十年,神經(jīng)科學和非線性科學相互融合滲透,形成了新興的神經(jīng)動力學。神經(jīng)系統(tǒng)呈現(xiàn)出了多種的非線性動力學行為,而在神經(jīng)動力學里其電活動也起到了舉足輕重的作用。神經(jīng)系統(tǒng)通過豐富的神經(jīng)放電節(jié)律來接收、傳遞和加工信息。周期、混沌、隨機神經(jīng)放電節(jié)律都是神經(jīng)放電的一般基本形式,因此,識別非周期神經(jīng)放電節(jié)律是混沌還是隨機一直是一個重要的科學問題。 本文以非線性動力學的理論為基礎,將數(shù)學,物理學與生命科學的知識相結(jié)合,搭建理論模型,運用計算機數(shù)值模擬仿真的方法,研究了一類位于加周期分岔中的貌似混沌的隨機神經(jīng)放電節(jié)律,經(jīng)過分析揭示了此類節(jié)律所具有的確定性機制和隨機性機制,還研究了陣發(fā)混沌神經(jīng)簇放電與峰放電的非光滑性,通過將其與典型的Ⅰ型和Ⅴ型陣發(fā)作比較,以此揭示其自身非光滑性的特點。 第1章首先介紹了非線性科學的概念和發(fā)展以及在神經(jīng)系統(tǒng)研究中非線性動力學的應用；其次講述了混沌理論的研究現(xiàn)狀與進展,還有在神經(jīng)系統(tǒng)中關于混沌的研究,包括國內(nèi)學者的研究對神經(jīng)放電中混沌的發(fā)展也起到了巨大的推動作用；最后概括介紹了本文的研究內(nèi)容。 第2章介紹了本文的一些基本概念與基本知識,主要有：可興奮細胞及其類型,神經(jīng)元的概念,神經(jīng)元的結(jié)構(gòu)和類型,神經(jīng)元動作電位的概念及其產(chǎn)生機制,神經(jīng)元放電的數(shù)學模型,時間序列分析方法,非線性動力學與生物學的對應等。 第3章在神經(jīng)起步點實驗中發(fā)現(xiàn)了一類介于周期k和周期k+1(k=1,2)節(jié)律之間非周期自發(fā)放電節(jié)律,其行為是長串的周期k簇和周期k+1簇的交替。確定性理論模型Chay模型展示出了周期k和周期k+1節(jié)律的共存行為。噪聲在共存區(qū)誘發(fā)出了與實驗結(jié)果類似的非周期節(jié)律,說明了該類節(jié)律是噪聲引起的兩類簇的躍遷。非線性預報及其回歸映射揭示該節(jié)律具有確定性機制；將兩類簇分別轉(zhuǎn)換為0和1得到一個二進制序列,對該序列進行概率分析獲得了兩類簇躍遷的隨機機制。這說明此節(jié)律是具有確定性結(jié)構(gòu)的隨機節(jié)律而不是混沌。 第4章選取了確定性Chay模型在固定參數(shù)下,采用數(shù)值仿真的方法來研究周期3陣發(fā)混沌神經(jīng)簇放電和峰放電的非光滑特性。通過分別計算兩種陣發(fā)混沌首次,三次回歸映射的導數(shù)和平均層流相長度,利用最小二乘法進行線性擬合,并將這兩種陣發(fā)混沌的標度率與光滑系統(tǒng)產(chǎn)生的Ⅰ型陣發(fā)和非光滑系統(tǒng)產(chǎn)生的V型陣發(fā)進行比較,發(fā)現(xiàn)其標度率介于Ⅰ型陣發(fā)與Ⅴ型陣發(fā)之間。 第5章給出了本文的結(jié)論。
[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，

本文編號：2485587