2000 Fiscal Year Final Research Report Summary
Global structure of traveling waves in 3-component competition-diffusion systems
| Project/Area Number |
11640107
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Toyama University |
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Principal Investigator |
IKEDA Hideo Toyama University, Science, Associated Professor, 理学部, 助教授 (60115128)
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| Co-Investigator(Kenkyū-buntansha) |
FUJITA Yasuhiro Toyama University, Science, Associated Professor, 理学部, 助教授 (10209067)
YOSHIDA Norio Toyama University, Science, Professor, 理学部, 教授 (80033934)
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| Project Period (FY) |
1999 – 2000
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| Keywords | reaction-diffusion systems / 3 competing species model / traveling waves / singular perturbation method / bifurcation phenomena / stability property |
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| Research Abstract |
Traveling wave solutions of three-component systems with competition and diffusion are considered. It is assumed that the first and second species move quite solwly relative to the third one. Other parameters in reaction terms are fixed to satisfy the following : When the first species is absent, the second and third ones can coexist stably and when the second one is absent, the first and third ones can also coexist stably. That is, we assume the above systems are bistable. First, we show the existence and stability of traveling wave solutions which connect two stable states. When we colide these stable traveling wave solutions each other on the one-dimensional line, we show that there are two categories depending on parameters : One is blocking phenomena, that is, they are blocked by a stable standing pulse solution. The other is annihilation, that is, they annihilate and then recover the stable state. Next we introduce a time constant to the first and second equations. For these systems with some parameters, we show there exist multiple traveling front solutions and study their stability properties. Finally we study the stability of planar traveling wave solutions on the two-dimensional plane and show that there are also two categories depending on parameters : One is stable, and the other is unstable and their interfaces become complicated.
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Research Products
(13 results)
