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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/80152Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Yi-Yun Lee | en |
| dc.contributor.author | 李一耘 | zh_TW |
| dc.date.accessioned | 2022-11-23T09:28:55Z | - |
| dc.date.available | 2021-07-23 | |
| dc.date.available | 2022-11-23T09:28:55Z | - |
| dc.date.copyright | 2021-07-23 | |
| dc.date.issued | 2021 | |
| dc.date.submitted | 2021-07-05 | |
| dc.identifier.citation | [1] P. N. Brown. Decay to uniform states in competitive systems. SIAM Journal on Mathematical Analysis, 14(4):659–673, 1983. [2] P. de Mottoni. Qualitative analysis for some quasilinear parabolic systems. Inst. Math. Pol. Acad. Sci. Zam, 1979. [3] R. A. Gardner. Existence and stability of travelling wave solutions of competition models: a degree theoretic approach. Journal of Differential equations, 44(3):343–364, 1982. [4] Y. KanOn. Parameter dependence of propagation speed of travelling waves for competition diffusion equations. SIAM journal on mathematical analysis, 26(2):340–363, 1995. [5] C. Muratov. A global variational structure and propagation of disturbances in reaction diffusion systems of gradient type. Discrete Continuous Dynamical SystemsB, 4(4):867, 2004. [6] M. Rodrigo and M. Mimura. Exact solutions of a competition diffusion system. Hiroshima Mathematical Journal, 30(2):257–270, 2000. [7] Vol’pert, Aĭzik Isaakovich, V. A. Volpert, and V. A. Volpert. Traveling wave solutions of parabolic systems, volume 140. American Mathematical Soc., 1994. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/80152 | - |
| dc.description.abstract | 我們用改良過後的算法做生物競爭模型Lotka-Volterra model 強競爭的數值模擬，使得我們可以保留行波解的資訊與觀察到一般解收斂至行波解的行為，甚至可以定義出一般解的廣義傳遞速度。藉由特定例子中，理論解與數值解的誤差分析，我們可以以可控制的誤差用一般解的漸進行為逼近解不出確切形式的行波解。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-23T09:28:55Z (GMT). No. of bitstreams: 1 U0001-2906202117435500.pdf: 1255902 bytes, checksum: 42464c57efcbe9ae0d1c90aa302b0bc8 (MD5) Previous issue date: 2021 | en |
| dc.description.tableofcontents | 摘要3 Abstract 5 Contents 7 List of Figures 9 Chapter 1 Introduction 11 Chapter 2 Survey 13 2.1 Diffusive LotkaVolterra Model . . . . . . . . . . . . . . . . . . . . 13 2.2 Traveling wave solution . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Variational method . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Chapter 3 Numerical scheme 19 3.1 Original model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Motion of numerical evolution solution . . . . . . . . . . . . . . . 21 3.3 Time-adjusting reference frame . . . . . . . . . . . . . . . . . . . . 24 Chapter 4 Simulation result and error analysis 27 4.1 Simulation for Huxley wave( gradient type model ) . . . . . . . . . . 28 4.2 Simulation for Lotka-Volterra model . . . . . . . . . . . . . . . . . . 30 4.3 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.4 Approximation of exact traveling wave solutions . . . . . . . . . . . 35 4.5 Local stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Chapter 5 Summary 43 Chapter 6 Future work 45 6.1 Proof of observation results . . . . . . . . . . . . . . . . . . . . . . 45 6.2 Generalization to other reaction diffusion models . . . . . . . . . . . 45 References 47 | |
| dc.language.iso | en | |
| dc.subject | 反應擴散方程 | zh_TW |
| dc.subject | 生物競爭模型 | zh_TW |
| dc.subject | 行波解 | zh_TW |
| dc.subject | traveling wave solution | en |
| dc.subject | diffusive Lotka-Volterra model | en |
| dc.subject | reaction diffusion system | en |
| dc.title | 生物競爭模型中傳遞速度的數值模擬 | zh_TW |
| dc.title | Numerical Propagation Speed in Diffusive Lotka-Volterra Model | en |
| dc.date.schoolyear | 109-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 夏俊雄(Hsin-Tsai Liu),薛克民(Chih-Yang Tseng),陳逸昆 | |
| dc.subject.keyword | 生物競爭模型,行波解,反應擴散方程, | zh_TW |
| dc.subject.keyword | diffusive Lotka-Volterra model,traveling wave solution,reaction diffusion system, | en |
| dc.relation.page | 47 | |
| dc.identifier.doi | 10.6342/NTU202101200 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2021-07-06 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| Appears in Collections: | 應用數學科學研究所 | |
Files in This Item:
| File | Size | Format | |
|---|---|---|---|
| U0001-2906202117435500.pdf | 1.23 MB | Adobe PDF | View/Open |
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