New approach to predict various oscillatory dynamics
| Project/Area Number |
20540116
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Meiji University (2011)
Osaka University (2008-2010) |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
KUWAMURA Masataka 神戸大学, 発達科学部, 准教授 (30270333)
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ウェーブ不安定化 / 反応拡散系 / 3重退化分岐 / 擬似回転波 / 分岐解析 / 0-1-2モード相互作用 / ウェーブ不定化 / 不変トーラス / 球面対称標準形 / ウェーブ分岐 / 時空間パターン / チューリング不安定 / ホップ分岐 / 球面対称性 |
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| Research Abstract |
Normal form for a wave instability under SO(2) symmetry is studied to understand oscillatory patterns for 3-component reaction-diffusion equations on a sphere. It turns out that there are rotating and standing waves in the case of lower mode instabilities and stabilities for both solutions are studied. Another possibilities for oscillatory patterns are also discussed. It turns out that 3-component RD system can have 1-2-3 triple modes degeneracy and its normal form was obtained. Normal form analysis shows that there is Hopf bifurcation point from 1-mode stationary solution.
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Report
(6 results)
Research Products
(25 results)
