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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/5868

    Title: 某些網格型微分方程的動態行為、腦資訊的非線性分析
    Other Titles: Dynamics of Some Types of Lattice Differential Equations and Nonlinear Analysis of Brain Information
    Authors: 楊定揮
    Contributors: 淡江大學數學學系
    Keywords: 混合型網格微分方程組;腦動態系統;單調行進波解;有限差分法;相關維度;;神經網路;延遲座標;嵌入定理;Lyapunov指數;同步
    Date: 2006
    Issue Date: 2009-03-16 13:11:54 (UTC+8)
    Abstract: 在混合型(with delayed and advanced term)網格微分方程組(Lattice Differential Equations)方面,在有限個神經元,考慮週期解的存在、唯一性及穩定性,及當有外力(forcing term)時,系統會有何分歧現象;在一維無窮個神經元,我們研究在不同的耦合係數、不同的時間遲滯、非線性項有兩類:monostable type (Fisher type or KPP type)及bistable type (Nagumo type)之下,單調行進波解(Traveling Wavefront Solution,TWS)的存在性、唯一性及穩定性,同時並考慮數值計算,所需用到的finite difference method 及continuation method。 關於Nonlinear Analysis of Brain Dynamics方面我們要利用Dynamical Systems及Neural Network的理論來計算實驗所量得的人類大腦實驗數據並做modeling。Dynamical Systems的方法包括了資料處理及度量複雜性裡相關的特徵值兩部分;其中資料處理包括了delay coordinate和embedding theory等方法,複雜性度量裡相關的特徵值,包含了correlation dimension、Lyapunov exponents、entropy、synchronization及phase synchronization等。希望藉由所計算出來的特徵值(D2, Entropy, Lyapnunov Exponents)改變,應用在臨床醫學方面,能在病人發病早期的過渡時期,及早發現,及早治療。Neural Network的方面,記錄人體運動的整個時程,大腦狀態(D2, Entropy)的變化,用Neural Network的工具進而瞭解運動時,大腦的各系統在時間與空間交互作用的特性。
    Appears in Collections:[Graduate Institute & Department of Mathematics] Research Paper

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