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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/20045完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全 | |
| dc.contributor.author | Ting-Yang Hsiao | en |
| dc.contributor.author | 蕭定洋 | zh_TW |
| dc.date.accessioned | 2021-06-08T02:39:13Z | - |
| dc.date.copyright | 2018-07-06 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-07-02 | |
| dc.identifier.citation | [1] R. A. Armstrong and R. McGehee, Competitive exclusion, Amer. Natur., 115 (1980), pp. 151–170.
[2] R. S. Cantrell and J. R. Ward, Jr., On competition-mediated coexistence, SIAM J. Appl. Math., 57 (1997), pp. 1311–1327. [3] C.-C. Chen and L.-C. Hung, A maximum principle for diffusive lotka-volterra systems of two competing species, J. Differential Equations, 261 (2016), pp. 4573–4592. [4] Nonexistence of traveling wave solutions, exact and semi-exact traveling wave solutions for diffusive Lotka-Volterra systems of three competing species, Commun. Pure Appl. Anal., 15 (2016),pp. 1451–1469. [5] C.-C. Chen, L.-C. Hung, and C.-C. Lai, An n-barrier maximum principle for autonomous systems of n species and its application to problems arising from population dynamics, submitted. [6] C.-C. Chen, L.-C. Hung, M. Mimura, M. Tohma, and D. Ueyama, Semi-exact equilibrium solutions for three-species competition-diffusion systems, Hiroshima Math J., 43 (2013), pp. 176–206. [7] C.-C. Chen, L.-C. Hung, M. Mimura, and D. Ueyama, Exact travelling wave solutions of threespecies competition-diffusion systems, Discrete Contin. Dyn. Syst. Ser. B, 17 (2012), pp. 2653–2669. [8] P. de Mottoni, Qualitative analysis for some quasilinear parabolic systems, Institute of Math., Polish Academy Sci., zam, 11 (1979), p. 190. [9] J.-S. Guo and C.-C. Wu, The existence of traveling wave solutions for a bistable three-component lattice dynamical system, J. Differential Equations, 260 (2016), pp. 1445–1455. [10] J.-S. Guo and C.-H. Wu, Wave propagation for a two-component lattice dynamical system arising in strong competition models, Journal of Differential Equations, 250 (2011), pp. 3504 – 3533. [11] Traveling wave front for a two-component lattice dynamical system arising in competition models, Journal of Differential Equations, 252 (2012), pp. 4357 – 4391. [12] S.-B. Hsu and T.-H. Hsu, Competitive exclusion of microbial species for a single nutrient with internal storage, SIAM J. Appl. Math., 68 (2008), pp. 1600–1617. [13] S. B. Hsu, H. L. Smith, and P. Waltman, Competitive exclusion and coexistence for competitive systems on ordered Banach spaces, Trans. Amer. Math. Soc., 348 (1996), pp. 4083–4094. [14] L.-C. Hung, Exact traveling wave solutions for diffusive Lotka-Volterra systems of two competing species, Jpn. J. Ind. Appl. Math., 29 (2012), pp. 237–251. [15] S. R.-J. Jang, Competitive exclusion and coexistence in a Leslie-Gower competition model with Allee effects, Appl. Anal., 92 (2013), pp. 1527–1540. [16] Y. Kan-on, Parameter dependence of propagation speed of travelling waves for competition-diffusion equations, SIAM J. Math. Anal., 26 (1995), pp. 340–363. [17] J. Kastendiek, Competitor-mediated coexistence: interactions among three species of benthic macroalgae, Journal of Experimental Marine Biology and Ecology, 62 (1982), pp. 201–210. [18] R. McGehee and R. A. Armstrong, Some mathematical problems concerning the ecological principle of competitive exclusion, J. Differential Equations, 23 (1977), pp. 30–52. [19] M. Mimura and M. Tohma, Dynamic coexistence in a three-species competition–diffusion system, Ecological Complexity, 21 (2015), pp. 215–232. [20] H. L. Smith and P. Waltman, Competition for a single limiting resource in continuous culture: the variable-yield model, SIAM J. Appl. Math., 54 (1994), pp. 1113–1131. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/20045 | - |
| dc.description.abstract | 這篇論文主要是探討離散以及非局部的洛特卡-沃泰爾拉競爭模型的物種質量估計。這篇文章中，我們使用N型屏障方法去證明離散以及非局部的洛特卡-沃泰爾拉模型的物種有一個有意思的下界。除此之外，我們利用這個下界，我們能夠證明某些條件下，三個物種的洛特卡-沃泰爾拉模型的解是不存在的。 | zh_TW |
| dc.description.abstract | In the present paper, we show that an analogous N-barrier maximum principle (see [3,5,7]) remains true for lattice systems. This extends the results in [3,5,7] from continuous equations to discrete and non-local equations. In order to overcome the difficulty induced by a discrete and non-local version of the classical diffusion in the lattice and non-local systems, we propose a more delicate construction of the N-barrier which is appropriate for the proof of the N-barrier maximum principle for lattice systems. As an application of the discrete N-barrier maximum principle, we study a coexistence problem of three species arising from biology, and show that the three species cannot coexist under certain conditions. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T02:39:13Z (GMT). No. of bitstreams: 1 ntu-107-R04221011-1.pdf: 916492 bytes, checksum: 650c635efe7e3bf951dfa781913a5e85 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
致謝 ii 中文摘要 iii 英文摘要 iv Introduction and main results 1 Preliminaries 8 Construction of the N-barrier for forward difference operator 29 Proof of the Discrete NBMP 34 Nonexistence of three species 39 Appendix 42 Non-Local Lotka-Volterra System 46 參考資料 47 | |
| dc.language.iso | en | |
| dc.title | 離散和非局部競爭型洛特卡－沃爾泰拉系統的行波解之物種數量估計 | zh_TW |
| dc.title | Estimates of Population Sizes for Traveling Wave Solutions of Discrete and Non-local Lotka-Volterra Competition Systems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王振男,林太家 | |
| dc.subject.keyword | 洛特卡-沃泰爾拉競爭模型,N型屏障法,離散洛特卡-沃泰爾拉模型,非局部的洛特卡-沃泰爾拉模型,最大值定理,行波解,總質量估計, | zh_TW |
| dc.subject.keyword | Lotka-Volterra System,Maximum principle,N-barrier method,Discrete Lotka-Volterra System,Non-Local Lotka-Volterra System,Traveling wave solution,Total mass estimate, | en |
| dc.relation.page | 46 | |
| dc.identifier.doi | 10.6342/NTU201801249 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2018-07-03 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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