2022 Fiscal Year Final Research Report
Mathematical and numerical analysis of interfacial dynamics arising in population models
| Project/Area Number |
18K03412
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
矢崎 成俊 明治大学, 理工学部, 専任教授 (00323874)
中村 俊子 (荻原俊子) 城西大学, 理学部, 教授 (70316678)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | 個体群動態モデル / 界面ダイナミクス / 移動境界問題 / 進行波 / 順序保存力学系 |
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| Outline of Final Research Achievements |
To understand the dynamics of interfaces and free boundaries that appear as boundaries between habitats dominated by different species in various population models describing the spatio-temporal dynamics of population densities, we conducted research using mathematical and numerical methods in a complementary manner. In particular, we clarified the parameter conditions for determining the sign of the propagating speed of bistable traveling waves in the Lotka-Volterra competition-diffusion system and obtained new results that will lead to controlling the habitat expansion of invasive alien species.
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| Free Research Field |
応用解析学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究において，競合関係にある生物種の個体数密度の時間変化を記述する多種ロトカ・ヴォルテラ競争拡散系に対し，双安定進行フロント波の速度やジャンクションを有する複雑な領域におけるフロント波の通過／停止条件に関する定量的な評価を行い，地球規模の重要な問題となっている侵略的外来種の侵入・定着を制御する方法に関する理論に裏付けられた知見を得ることができ，学術的のみならず社会的にも意義のある成果が得られた．
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