遲滯型細胞神經網絡行進波之結構

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林嫺雯(Shian-Wen Lin) 查詢紙本館藏

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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)

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摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 細胞神經網絡
★ 行進波

關鍵字(英)

★ cellular neural networks
★ traveling waves

論文目次

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

參考文獻

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指導教授

許正雄(Cheng-Hsiung Hsu)

審核日期

2003-6-29

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