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研究生: 林嫺雯
Shian-Wen Lin
論文名稱: 遲滯型細胞神經網絡行進波之結構
Structure of Traveling Waves in Delayed Cellular Neural Networks
指導教授: 許正雄
Cheng-Hsiung Hsu
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
畢業學年度: 91
語文別: 英文
論文頁數: 29
中文關鍵詞: 細胞神經網絡行進波
外文關鍵詞: cellular neural networks, traveling waves
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  • 這篇論文主要研究,在一個維度上,遲滯型細胞神經網絡
    (CNN)行進波解的結構。利用Monotone Iteration 及
    Shooting的方法我們可以證明行進波之解結構隨著速度的改變而有不同的行為。


    This thesis is concerned with the global structure of traveling waves
    for one-dimensional cellular neural networks with distributed delayed signal
    transmission. By using the monotone iteration method and shooting
    method, we describe the transition of wave profiles from monotonicity,
    damped oscillation, periodicity, unboundedness and back to monotonicity
    as the wave speed is varied.

    Abstract.........................................................................1 1. Introduction.............................................................2 2. Properties of Characteristic Equation.....................5 3. Existence of Monotonic Traveling Waves................7 3.1. Construction of Upper and Lower Solutions.....7 3.2. Monotone Iteration Method.............................11 3.3. Proof of Main Theorem (I)..............................14 4. Structure of Non-Monotonic Traveling Waves.......15 4.1. Basic Properties of Asymptotic Initial Value Problem...................................................................15 4.2. Proof of Main Theorem (II)............................26 References.....................................................................28

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