New theory for transient dynamics in reaction-diffusion systems allowing collapse of attractors
| Project/Area Number |
24654044
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Global analysis
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| Research Institution | Ryukoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Kanako 茨城大学, 理学部, 准教授 (10451519)
KUWAMURA Masataka 神戸大学, 人間発達環境学研究科, 教授 (30270333)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 遷移ダイナミクス / 反応拡散系 / 大域アトラクタ / アトラクタの崩壊 / 散逸力学系 / 保存則 / 摂動系 / チューリング的パターン / 反応拡散方程式系 / 無限次元力学系 / 保存則のある反応拡散系 / 大域的アトラクタ / パターン形成 / 応用解析 |
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| Outline of Final Research Achievements |
We consider reaction-diffusion systems having a global attractor which collapses and turns to be a single stationary state by a perturbation. Although the dynamical structure largely changed by the perturbation, there is a perturbed orbit close to the unperturbed one during a transient time. In a specific reaction-diffusion system with conservation law we show for the perturbed system that a Turing-like wave takes place and it changes to a single spike, then the pattern finally collapses. The perturbed system has no longer steady state solutions which induce a Turing type instability. Nonetheless in the transient dynamics such a Turing-like pattern can be shown.
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Report
(4 results)
Research Products
(22 results)
