Reaction Diffusion Dynamics in non-homogeneous media
| Project/Area Number |
20540212
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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 |
Global analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
SAKAMOTO Kunimoch Hiroshima University, 大学院・理学研究科, 教授 (40243547)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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 | パターンダイナミクス / 反応拡散系 / 曲率 / 固有値 / 安定性 / 対称性 / パターンダイナミク / 非正常分岐現象 / 周期解 / Turing不安定性 / 波動分岐 / 領域境界の曲率 / 曲率の非一様性 / 空間周期解 / 安定性・軌道安定性 / 反応拡散方程式系 / Riemann計量と非一様拡散 / Fokker-Planck方程式 / 非一様場 / 特異極限 |
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| Research Abstract |
Fokker-Planck equations that describe the evolution of phase distributions in coupled oscillators were treated under an asymmetric natural frequency distribution. We found that the destabilization of the trivial distribution is of Hopf bifurcation type. The stability of layered solutions in reaction-diffusion equations was investigated, when the interface of the layered solution intersects the boundary of the domain. The stability is determined by the relative order between the curvature of the intersecting region and the Steklov eigenvalues of the Laplacian. A theoretical foundation of the Turing instability in 3-component reaction diffusion systems was established. The essence of the Turing instability lies in the existence of unstable subsystems within a stable full system and that the diffusion rates of unstable subsystems are relatively small compared with those of the complimentary subsystems. Two types of Turing instability were identified, according to types of instability of unstable subsystems.
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Report
(4 results)
Research Products
(18 results)
