| Project/Area Number |
12640217
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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 |
Global analysis
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| Research Institution | Yokohama City University |
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Principal Investigator |
EI Shin-ishiro Yokohama City University, Graduate School of Integrated Science, associate professor, 総合理学研究科, 助教授 (30201362)
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| Co-Investigator(Kenkyū-buntansha) |
MIZUMACHI Tetsu Yokohama City University, Graduate School of Integrated Science, associate Professor, 総合理学研究科, 助教授 (60315827)
SHIRAISHI Takaaki Yokohama City University, Graduate School of Integrated Science, Professor, 総合理学研究科, 教授 (50143160)
FUJII Kazuyuki Yokohama City University, Graduate School of Integrated Science, Professor, 総合理学研究科, 教授 (00128084)
TAKEMURA Kouichi Yokohama City University, Graduate School of Integrated Science, research association, 総合理学研究科, 助手 (10326069)
YANAGIDA Eiji Tohoku University, Faculty of Science, Professor, 大学院・理学研究科, 教授 (80174548)
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| Project Period (FY) |
2000 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2000: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | reaction-diffusion systems / pulse dynamics / pulse interaction / bifurcation structure / self-replication / elastic reflection of pulses / 欠陥のダイナミクス / 分岐点 / 反応拡散方程式 / パルス解 / 自己複製 / 粒子的反射 / 非線形発展方程式 / 中心多様体 / 弱い相互作用 / 粒子的反射運動 / 特異点 / 脈動的進行パルス |
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| Research Abstract |
In this project, we considered the localized patterns in reaction-diffusion systems and tried to establish the theories to analyze the time evolutional behaviors. As the consequence, we obtained several results for the systems in 1D problems such as the bifurcation structures and pulse interactions. Explicitly speaking, he tails of pulse-like localized patterns are exponentially decaying, then we derived the equations describing the motion of interacting pulses as well as the mathematical validity. Moreover, by considering them in the neighborhood of bifurcation points and applying the standard center manifold theory together with pulse interaction methods, we could analyze various complex behaviors of pulses such as self-replication and reflection of pulses. For example, in self-replicating phenomena, we could show the existence of critical distances such that pulses begin to split when distances between pulses are beyond the critical one. It is expected to explain the basis of spatially periodic patterns.
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