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| Title: | 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 |
| Authors: | 王靜慧
Wang, Ching-Hui |
| Contributors: | 符聖珍
王靜慧
Wang, Ching-Hui |
| Keywords: | 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 |
| Date: | 2021 |
| Issue Date: | 2021-07-01 19:51:28 (UTC+8) |
| Abstract: | 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. |
| Reference: | [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. |
| Description: | 博士
國立政治大學
應用數學系
100751501 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0100751501 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202100501 |
| Appears in Collections: | [應用數學系] 學位論文
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| 150101.pdf | | 1609Kb | Adobe PDF2 | 9 | View/Open |
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