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2017 Fiscal Year Final Research Report

Hierarchical structures and robustness for the set of global solution branches of spatially localized patterns in dissipative systems

Research Project

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Project/Area Number 26247015
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionTohoku University

Principal Investigator

Nishiura Yasumasa  東北大学, 材料科学高等研究所, 特任教授 (00131277)

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)
Project Period (FY) 2014-04-01 – 2018-03-31
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
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.

Free Research Field

応用数学

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Published: 2019-03-29  

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