政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/135979

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/135979

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | 全文筆數/總筆數 : 115726/146760 (79%)
造訪人次 : 56391454 線上人數 : 519

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

搜尋範圍

查詢小技巧：

您可在西文檢索詞彙前後加上"雙引號"，以獲取較精準的檢索結果

若欲以作者姓名搜尋，建議至進階搜尋限定作者欄位，可獲得較完整資料

進階搜尋

主頁 ‧ 登入 ‧ 上傳 ‧ 說明 ‧ 關於政大典藏 ‧ 管理

到手機版

政大機構典藏 > 理學院 > 應用數學系 > 學位論文 > Item 140.119/135979

請使用永久網址來引用或連結此文件: https://nccur.lib.nccu.edu.tw/handle/140.119/135979

題名:	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
作者:	王靜慧 Wang, Ching-Hui
貢獻者:	符聖珍王靜慧 Wang, Ching-Hui
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 Reaction-diffusion system Traveling wave solution Predator-prey system Holling-Tanner model Beddington-DeAngelis functional response Ratio- Dependent functional response
日期:	2021
上傳時間:	2021-07-01 19:51:28 (UTC+8)
摘要:	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.
參考文獻:	[1] S. AI, Y. DU, and R. PENG, Traveling waves for a generalized Holling–Tanner predator–prey model, J. Differ. Eqn., 263 (2017), pp. 7782–7814. [2] I. BARBALAT, Systemes déquations différentielles dóscillations non linéaires, Rev. Math. Pures Appl., 4 (1959), pp. 267–270. [3] Y.-Y. CHEN, J.-S. GUO, and C.-H. YAO, Traveling wave solutions for a continuous and discrete diffusive predator–prey model, J. Math. Anal. Appl., 445 (2017), pp. 212– 239. [4] Y. DU and S.-B. HSU, A diffusive predator–prey model in heterogeneous environment, J. Differ. Eqn., 203 (2004), pp. 331–364. [5] S.-C. FU, Traveling waves for a diffusive SIR model with delay, J. Math. Anal. Appl., 435 (2016), pp. 20–37. [6] S.-C. FU, M. MIMURA, and J.-C. TSAI, Traveling waves in a hybrid model of demic and cultural diffusions in Neolithic transition, J. Math. Biol., 82 (2021), p. article 26. [7] J. K. HALE, Ordinary Differential Equations, R.E. Krieger Publ., (1980). [8] W.-T. LI, G. LIN, and S. RUAN, Existence of travelling wave solutions in delayed reaction–diffusion systems with applications to diffusion–competition systems, Nonlinearity, 19 (2006), pp. 1253–1273. [9] C.-H. WANG and S.-C. FU, Traveling wave solutions to diffusive Holling-Tanner predatorprey models, Discrete Cont. Dyn.-B, 26 (2021), pp. 2239–2255. [10] X.-S. WANG, H. WANG, and J. WU, Traveling waves of diffusive predator-prey systems: disease outbreak propagation, Discrete Cont. Dyn. S., 32 (2012), pp. 3303–3324. [11] W. ZUO and J. SHI, Traveling wave solutions of a diffusive ratio-dependent Holling-Tanner system with distributed delay, Commun. Pur. Appl. Anal., 17 (2018), pp. 1179–1200.
描述:	博士國立政治大學應用數學系 100751501
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0100751501
資料類型:	thesis
DOI:	10.6814/NCCU202100501
顯示於類別:	[應用數學系] 學位論文

文件中的檔案:

檔案	描述	大小	格式	瀏覽次數
150101.pdf		1609Kb	Adobe PDF2	11	檢視/開啟

在政大典藏中所有的資料項目都受到原著作權保護.

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

DSpace Software Copyright © 2002-2004 MIT & Hewlett-Packard / Enhanced by NTU Library IR team Copyright © - 回饋