2010 Fiscal Year Final Research Report
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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| 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 |
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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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