2013 Fiscal Year Final Research Report
Turing's Diffusion-Driven-Instability Revisited-from a view point of global structure of solution sets
| Project/Area Number |
24654037
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
TAKAGI Izumi 東北大学, 理学(系)研究科(研究院), 教授 (40154744)
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| Project Period (FY) |
2012-04-01 – 2014-03-31
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| Keywords | 反応拡散系 / 拡散誘導不安定化 / パターン形成 / 定常解集合の大域構造 |
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| Research Abstract |
To explain how a spatial structure is autonomously formed in the embryogenesis, Turing proposed the notion of "Diffusion-Driven-Instability" (DDI, for short), which says that when two chemicals with different diffusion rates react each other, spatially homogeneous states may be destabilized and nontrivial spatial structure emerges as a result. Mathematically, this is considered as bifurcation of nonconstant steady-state solutions from a constant stationary solution. In this project we showed patterns can be formed without bifurcation from a constant stationary solution, and proposed a new interpretation of Turing's DDI.
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