### 博碩士論文 90221004 詳細資訊

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(Structure of Traveling Waves in Delayed Cellular Neural Networks)

 ★ 遲滯型細胞神經網路之行進波 ★ 網格型微分方程的行進波的數值解 ★ 某類網格型微分方程行波解的存在性，唯一性及穩定性 ★ 某類週期性網格型微分方程行波解之研究 ★ 網格型動態系統行波解之研究 ★ 矩陣值勢能上的sofic測度 ★ 在Sofic Shift上的多重碎型分析 ★ 某類傳染病模型微分方程行波解之研究 ★ 某類三維癌症模型之整體穩定性分析 ★ 三種競爭合作系統之行波解的存在性 ★ 離散型Lotka-Volterra競爭系統之行波解的穩定性

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(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。

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.

★ 行進波

★ traveling waves

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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