| Project/Area Number |
16H07254
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Meiji University |
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Principal Investigator |
Contento Lorenzo 明治大学, 研究・知財戦略機構, 研究推進員 (50782562)
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| Research Collaborator |
Mimura Masayasu
Hilhorst Danielle
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| Project Period (FY) |
2016-08-26 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | mathematical modelling / competition-diffusion / pattern formation / travelling wave / competitive exclusion / species coexistence / singular limit / traveling waves / 数理生態学 / 競争緩和共存 / 競争拡散方程式系 / 進行波解 / 特異極限 |
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| Outline of Final Research Achievements |
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species can be modelled by a three-species competition-diffusion system. We have proved rigorously that when the invader is very strong it will always be able to replace the native species, while it will never survive in the new environment if it is sufficiently weak. In the intermediate cases, coexistence occurs in complex spatio-temporal patterns, such as regular or breathing spirals, periodic multi-core spiral patterns or chaotic spiral turbulence. The origin of and transition between such patterns lies in the interaction of two planarly stable fronts. By studying the bifurcation structure of their one-dimensional equivalent (travelling waves), we can also understand the mechanisms governing the two dimensional case.
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| Academic Significance and Societal Importance of the Research Achievements |
We have shown how complex spatio-temporal patterns can arise from the interaction of two planarly stable fronts, without the need for instability as in other reaction-diffusion models. We have given rigorous results on the system's limit behaviour even if no vector comparison principle holds.
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