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| 研究生： |
王靜慧 Wang, Ching-Hui |
|---|---|
| 論文名稱： |
一些具擴散項的霍林-坦納捕食者-被捕食者模型的行波解 Traveling Wave Solutions of Some Diffusive Holling-Tanner Predator-Prey Models |
| 指導教授： | 符聖珍 |
| 口試委員: |
班榮超
曾睿彬 劉宣谷 吳昌鴻 符聖珍 |
| 學位類別： |
博士
Doctor |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2021 |
| 畢業學年度： | 109 |
| 語文別： | 英文 |
| 論文頁數： | 49 |
| 中文關鍵詞： | 反應擴散系統 、行波解 、捕食者－被捕食者系統 、霍林-坦納模型 、貝丁頓-迪安傑利斯功能反應 、比率相關功能反應 |
| 外文關鍵詞： | Reaction-diffusion system, Traveling wave solution, Predator-prey system, Holling-Tanner model, Beddington-DeAngelis functional response, Ratio- Dependent functional response |
| DOI URL： | http://doi.org/10.6814/NCCU202100501 |
| 相關次數： | 點閱：67 下載：4 |
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在本文中，我們首先確立了一個具擴散項的廣義霍林-坦納(Holling-Tanner) 捕食者-被捕食者模型的半行波解之存在，該模型的功能反應可能同時取決於捕食者和被捕食者的族群。接下來，利用建構利亞普諾夫(Lyapunov) 函數和引用前面所獲得的半行波解，我們證明了此種模型在不同功能反應下行波解亦存在，這些功能反應包含洛特卡－沃爾泰拉(Lotka-Volterra) 型、霍林二型(Holling II) 以及貝丁頓-迪安傑利斯(Beddington-DeAngelis)型。最後，通過上下解方法，我們也證實了具有比率依賴功能反應的擴散霍林-坦納捕食者－被捕食者模型的半行波解存在。然後，藉由分析此半行波解在無限遠處的上、下極限，證明了行波解的存在。
In this thesis, we first establish the existence of semi-traveling wave solutions to a diffusive generalized Holling-Tanner predator-prey model in which the functional response may depend on both the predator and prey populations.
Next, by constructing the Lyapunov function, we apply the obtained result to show the existence of traveling wave solutions to the diffusive Holling-Tanner predator-prey models with various functional responses, including the Lotka-Volterra type functional response, the Holling type II functional response, and the Beddington-DeAngelis functional response.
Finally, we establish the existence of semi-traveling wave solutions of a diffusive Holling-Tanner predator-prey model with the Ratio-Dependent functional response by using the upper and lower solutions method. Then, by analyzing the limit superior and limit inferior of the semi-traveling wave solutions at infinity, we show the existence of traveling wave solutions.
致謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Figures vi
1 Introduction 1
2 Semi-traveling wave solutions to system (1.5) 7
2.1 Non-existence of semi-traveling wave solutions 7
2.2 The modified system 8
2.3 Proof of Theorem 1.1 15
3 Traveling wave solution to system (1.3) 18
3.1 Proof of Theorem 1.2 and Theorem 1.3 18
3.2 Numerical simulation results 25
4 Traveling wave solutions to system (1.9) 28
4.1 A general system 28
4.2 Upper and lower solutions to system (1.10) 30
4.3 Semi-traveling wave solutions to system (1.9) 38
4.4 Proof of Theorem 1.4 41
4.5 Numerical simulation results 44
Appendix 46
Bibliography 48
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