動態車流模式混沌行為發生機制之研究

Abstract

本文利用混沌理論來探討動態車流模式之混沌現象,這是一個分析動 態車流模式的新方法.首先,利用離散化之技巧可以從原方程式得到一個非 線性方程式系統組,接著利用動態理論的方法去探討此一非線性方程式系 統組之行為.利用離散的動態方法去研究交通波動方程式混沌現象是這個 方法的主要概念.根據交通波動方程式之擴散與混沌特性,則此方法有兩個 重要的特性,第一,此方法提供了一個研究交通車流模式之新觀點,換言之, 此方法可以探索交通波動方程式之混沌現象,第二,與傳統的分析方法比 較,則此方法可以直接找出導致車流不穩定之混沌區間.探討不同邊界條件 與所求得之數值結果在本文中有詳細的說明與分析,數值結果提供了模式 存在奇異吸子之證據,且會存在一個模式之擴散係數臨界值,而當擴散係數 大於臨界值時,車流模式會是一個穩定的狀態,而當擴散係數小於臨界值 時,則車流模式會失去穩定狀態,且模式之解的軌跡會是一個奇異吸子. In this thesis, a new approach to analysis chaotic phenomena of dynamic traffic model is presented. We study the traffic wave equations by using chaotic theory. Firstly, a discretization procedure is applied to discretize the traffic wave equation from which a system of nonlinear algeraic equations is obtained. Then, dynamic method is applied to solve the system of the nonlinear algeraic equations. The main concept of this method is that it takes basic chaotic perty of traffic wave equation, and studies the equation by using discretized ynamic method. Based on the fact of a diffusive and chaotic property of traffic wave equation, the proposed new approach has several important properties. Firstly,it provides a new dynamic point of view for traffic flow model. In other words,it explores the chaotic phenomena of traffic wave equation precisely. Secondly, by comparing with a trditional method, this method can find out the unstable region directly.A standard traffic flow model problem under various boundaryconditions has been successfully implemented and several typical numerical results of this model problem are demonstrated and discussed. The results provide evidence for the existence of strange attractors. It shown that there is a critical value above which the solution of the dynamic traffic model is stable and below which the motion becomes highly unstable.