2017 Fiscal Year Final Research Report
Hierarchical structures and robustness for the set of global solution branches of spatially localized patterns in dissipative systems
| Project/Area Number |
26247015
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
長山 雅晴 北海道大学, 電子科学研究所, 教授 (20314289)
平岡 裕章 東北大学, 材料科学高等研究所, 教授 (10432709)
國府 寛司 京都大学, 理学研究科, 教授 (50202057)
上田 肇一 富山大学, 大学院理工学研究部(理学), 准教授 (00378960)
中田 聡 広島大学, 理学研究科, 教授 (50217741)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | パターン形成 / 散逸構造 / パルス波 / 自己組織化 / トポロジー / ネットワーク / 反応拡散方程式 |
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| Outline of Final Research Achievements |
Spatially localized patterns in dissipative systems form an important class of solutions in pattern formation theory. To understand the generation, annihilation and collision dynamics among those patterns is a big challenge. Global structure of all relevant solution branches forms a hierarchical structure and its connecting manner of stable/unstable manifolds gives an insight for dynamic behaviors of the above exotic dynamics. We applied the methodology to localized convective patterns of binary fluid and three component reaction diffusion systems of FitzHugh-Nagumo type.
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| Free Research Field |
応用数学
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