離散型Lotka-Volterra競爭系統之行波解的穩定性

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李閎嚴(Hung-Yen Lee) 查詢紙本館藏

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數學系

論文名稱

離散型Lotka-Volterra競爭系統之行波解的穩定性
(Stability of traveling wavefronts for a discrete Lotka-Volterra competition system)

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摘要(中)

本論文主要研究三物種競爭合作關係之離散型Lotka-Volterra 模型行波解的穩定性問題。透過能量加權方法以及比較原則，在較大的速度下，我們證明了行波解具有指數穩定的特性。

摘要(英)

In this thesis, we study the stability of traveling wave solutions for the three species competition cooperation system, which is the discrete version of the Lotka-Volterra system.
Applying the weighted energy method and the comparison principle, we can derive the result that the traveling wavefronts with large speed are exponentially stable.

關鍵字(中)

★ 穩定性
★ Lotka-Volterra

關鍵字(英)

★ stability
★ Lotka-Volterra

論文目次

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Some known results and background . . . . . . . . . . . . . . . . . . . . . 6
3 Stability for traveling wavefronts . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1 Weighted energy estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Derivative estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Proof of Theorem 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

參考文獻

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指導教授

許正雄(Cheng-Hsiung Hsu)

審核日期

2019-1-19

推文