遲滯型細胞神經網路似駝峰行進波之研究

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姓名

李俊憲(Chun-Hsien Li) 查詢紙本館藏

畢業系所

數學系

論文名稱

遲滯型細胞神經網路似駝峰行進波之研究
(On Camel-Like Traveling Wave Solutionsin Cellular Neural Networks with Distributive Delay)

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摘要(中)

這篇論文主要研究散佈在一維整數網格上的遲滯型細胞神經網路似駝峰行進波的種類。細胞元之間的動態行為除了有瞬時的自身回饋外，由於信號傳播轉換速度的關係，會與左邊最鄰近的m個細胞元產生遲滯相互作用。在本文中，我們使用階梯法直接勾勒出解析解的形式，並進一步證明除了單調行進波的存在性外，在某些適當條件下，亦存在似駝峰的非單調行進波。最後我們也搭配一些數值結果來驗證理論分析。

摘要(英)

In this thesis, we study the camel-like traveling wave solutions for a class of delayed cellular neural networks distributed in the one-dimensional integer lattice Z. The dynamics of a given cell is characterized by instantaneous
self-feedback and neighborhood interaction with its nearest m left neighbors with distributive delay due to, for example, finite switching speed and finite velocity of signal transmission.
Using the method of step, we can directly figure out the analytic solution and then prove that,
in addition to the existence of monotonic
traveling wave solutions, for certain templates there exist non-monotonic traveling wave solutions such as camel-like waves with many critical points. Some numerical results are also given.

關鍵字(中)

★ 網格動態系統
★ 似駝峰行進波
★ 遲滯型細胞神經網路
★ 階梯法

關鍵字(英)

★ lattice dynamical systems
★ camel-like traveling waves
★ method of step
★ delayed cellular neural networks

論文目次

Contents
˙Abstract ………………………………………………………………………1
˙Introduction …………………………………………………………………2
˙Construction of the solution formula …………………………………6
˙Proof of the main theorem ………………………………………………14
---3.1. Profiles for αj>0, 1≦j≦m ……………………………………15
---3.2. Profiles for αj<0, 1≦j≦m ……………………………………16
---3.3. Profiles for alternating αj with |αj|≧|αj+1| …………17
˙References …………………………………………………………………30

參考文獻

References
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指導教授

楊肅煜(Suh-Yuh Yang)

審核日期

2004-6-9

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