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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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥31,590,000 (Direct Cost: ¥24,300,000、Indirect Cost: ¥7,290,000)
Fiscal Year 2017: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Fiscal Year 2015: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Fiscal Year 2014: ¥11,830,000 (Direct Cost: ¥9,100,000、Indirect Cost: ¥2,730,000)
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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 / 応用数学 / 大域分岐 / 空間局在解 / 応用拡散方程式 / 階層性 / レジリエンス |
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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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Report
(5 results)
Research Products
(123 results)
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[Presentation] Pulse Generators2016
Author(s)
Yasumasa Nishiura
Organizer
The Fourth International Conference Nonlinear Waves - Theory and Applications
Place of Presentation
Tsinghua Univerisity, Beijing, China
Year and Date
2016-06-27
Related Report
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[Presentation] Influence of convection ot self-motion of camphor2015
Author(s)
Mamoru Okamoto, Masaharu Nagayama, Yasuaki Kobayashi, Mina Kaneko and Masakazu Akiyama
Organizer
The 16th RIES-Hokudai International Symposium "Jyutsu" (Poster Presentation)
Place of Presentation
Chateraise Gateaux Kingdom Sapporo (Hokkaido ,Sapporo)
Year and Date
2015-11-10
Related Report
Int'l Joint Research
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[Presentation] Mathematical modeling of proneural wave2015
Author(s)
Yoshiaki Minami, Masaharu Nagayama, Makoto Sato, Takashi Miura
Organizer
The 16th RIES-Hokudai International Symposium "Jyutsu" (Poster Presentation)
Place of Presentation
Chateraise Gateaux Kingdom Sapporo (Hokkaido, Sapporo)
Year and Date
2015-11-10
Related Report
Int'l Joint Research
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[Presentation] 自己駆動系で作るリズムと秩序2015
Author(s)
中田聡（広島大学），田 中晋平，長山雅晴
Organizer
日本応用数理学会年会
Place of Presentation
金沢大学角間キャンパス （石川県・金沢市）
Year and Date
2015-09-09
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