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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳俊全(Chiun-Chuan Chen) | |
| dc.contributor.author | Zhi-Hao Shi | en |
| dc.contributor.author | 施智皓 | zh_TW |
| dc.date.accessioned | 2022-11-23T09:12:00Z | - |
| dc.date.available | 2022-02-21 | |
| dc.date.available | 2022-11-23T09:12:00Z | - |
| dc.date.copyright | 2022-02-21 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-02-04 | |
| dc.identifier.citation | Ahmad Alhasanat and Chunhua Ou. “Minimal-speed selection of traveling waves to the Lotka–Volterra competition model”. In: Journal of differential equations 266.11 (2019), pp. 7357–7378. Ahmad Alhasanat and Chunhua Ou. “Stability of Traveling Waves to the Lotka-Volterra Competition Model”. In: Complexity 2019 (2019). Yousef Alqawasmeh and Frithjof Lutscher. “Persistence and spread of stage structured populations in heterogeneous landscapes”. In: Journal of mathematical biology 78.5 (2019), pp. 1485–1527. Xavier Belles. “MicroRNAs and the evolution of insect metamorphosis”. In: Annual Review of Entomology 62 (2017), pp. 111–125. Xavier Belles. “Origin and evolution of insect metamorphosis”. In: eLS (2011). SM Bouguima and FZ Mehlia. “Asymptotic behavior of an age-structured population model with diffusion”. In: J. Appl. Anal. Comput 2 (2012), pp. 351–362. Deniz F Erezyilmaz. “Imperfect eggs and oviform nymphs: a history of ideas about the origins of insect metamorphosis”. In: Integrative and Comparative Biology 46.6 (2006), pp. 795–807. Jian Fang, Yijun Lou, and JianhongWu. “Can pathogen spread keep pace with its host invasion?” In: SIAM Journal on Applied Mathematics 76.4 (2016), pp. 1633–1657. Peter Hammond. “Species Inventory”. In: Global Biodiversity: Status of the Earth’s Living Resources. Ed. by Brian Groombridge. Dordrecht: Springer Netherlands, 1992, pp. 17–39. isbn: 978-94-011-2282-5. doi: 10.1007/978-94-011-2282-5_4. url: https://doi.org/10.1007/978-94-011-2282-5_4. Yuzo Hosono. “The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model”. In: Bulletin of Mathematical Biology 60.3 (1998),pp. 435–448. Qihua Huang and Yuxiang Zhang. “Spread rates of a juvenile-adult population in constant and temporally variable environments”. In: Theoretical Ecology 14.1 (2021), pp. 145–160. Wenzhang Huang and Maoan Han. “Non-linear determinacy of minimum wave speed for a Lotka–Volterra competition model”. In: Journal of Differential Equations 251.6 (2011), pp. 1549–1561. Jarmila Kukalova-Peck. “Origin and evolution of insect wings and their relation to metamorphosis, as documented by the fossil record”. In: Journal of Morphology 156.1 (1978), pp. 53–125. Shengqiang Liu, Lansun Chen, and Ravi Agarwal. “Recent progress on stage structured population dynamics”. In: Mathematical and Computer Modelling 36.11-13 (2002), pp. 1319–1360. VHW Rudolf and Kevin D Lafferty. “Stage structure alters how complexity affects stability of ecological networks”. In: Ecology letters 14.1 (2011), pp. 75–79. Sebastian Schreiber and Volker HW Rudolf. “Crossing habitat boundaries: coupling dynamics of ecosystems through complex life cycles”. In: Ecology letters 11.6 (2008), pp. 576–587. James W Truman and Lynn M Riddiford. “The evolution of insect metamorphosis: a developmental and endocrine view”. In: Philosophical Transactions of the Royal Society B 374.1783 (2019), p. 20190070. Hans FWeinberger, Mark A Lewis, and Bingtuan Li. “Analysis of linear determinacy for spread in cooperative models”. In: Journal of Mathematical Biology 45.3 (2002), pp. 183–218. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/79805 | - |
| dc.description.abstract | 自然界中存在大量的物種生活史具有不同的生長階段(例如:青蛙與蝌蚪、蝴蝶與毛毛蟲等等)，特別是大約有近45-60%的昆蟲都具有階段性的生長史，而階段性的生長史可能意味著成體和幼體佔據不同的生態區位。為了從反應擴散方程的角度解釋這個現象，我們藉由Alhasanat 和Ou在2019年發展的上下解技巧證明了其行波解非線性速度選擇的條件，其生態含意是: 在此給定情形下，階段性生活史的物種總是更能夠加速其入侵弱勢物種的速度。在論文的最後，我們給出了比較階段性的生長史和簡單生長史競爭優勢的判據。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-23T09:12:00Z (GMT). No. of bitstreams: 1 U0001-3001202210585600.pdf: 757248 bytes, checksum: 583bfa10323b9cd156b5f1295655ef68 (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | "1 Modeling and main questions 1 1.1 When can a stage structured species take advantage of unstructured one? 1 1.2 Modeling and a generalization of reproduction number R0 2 1.2.1 Previous modeling of a stage-structured model with diffusion and R0 as a characteristic of its asymptotic behavior 2 1.2.2 Diffusive staged structured Lotka-Volterra model 4 1.2.3 Generalized fitness and reproduction number structured LV model 5 2 Previous results of speed selection mechanism 6 2.1 A general theory for linear determinacy of cooperative systems 6 2.2 Some previous studies in nonlinear speed selection of a LV model 9 3 Model with stage structure and its traveling wave solution 11 3.1 Equal ratio solution of uniform competition effect (without interspecific competition) 11 3.2 Speed selection mechanism of a diffusive stage-structured model 14 3.3 Speed selection mechanism of a diffusive stage-structured competitive Lotka-Volterra model (Main result) 16 3.3.1 Linear speed selection 17 3.3.2 Non-linear speed selection 22 4 Numerical simulations and ecological implications 32 4.1 Critical competition coefficient between linear and nonlinear speed selection 32 4.2 Conclusion 34 Appendices 36 A Proof and numerical method 37 A.1 Asymptotic behavior of the wave profile near (0,0,0) 37 A.2 Newton method on measuring the traveling wave speed 39" | |
| dc.language.iso | en | |
| dc.subject | 臨界競爭係數 | zh_TW |
| dc.subject | 行波解 | zh_TW |
| dc.subject | 階段性生活史 | zh_TW |
| dc.subject | 競爭型洛特卡－沃爾泰拉方程式 | zh_TW |
| dc.subject | 速度選擇機制 | zh_TW |
| dc.subject | stage-structured species | en |
| dc.subject | competitive Lotka- Volterra model | en |
| dc.subject | speed selection mechanism | en |
| dc.subject | critical competition coefficient | en |
| dc.subject | traveling wave solution | en |
| dc.title | 具階段性生活史之物種的反應擴散模型的行波解 | zh_TW |
| dc.title | Traveling wave solutions for a stage structure model | en |
| dc.date.schoolyear | 110-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 夏俊雄(Chen-Hsi Hsieh),王振男(An-Sheng Lee) | |
| dc.subject.keyword | 行波解,階段性生活史,競爭型洛特卡－沃爾泰拉方程式,速度選擇機制,臨界競爭係數, | zh_TW |
| dc.subject.keyword | traveling wave solution,stage-structured species,competitive Lotka- Volterra model,speed selection mechanism,critical competition coefficient, | en |
| dc.relation.page | 43 | |
| dc.identifier.doi | 10.6342/NTU202200261 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-02-08 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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|---|---|---|---|
| U0001-3001202210585600.pdf | 739.5 kB | Adobe PDF | 檢視/開啟 |
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