2013 Fiscal Year Final Research Report

Turing's Diffusion-Driven-Instability Revisited-from a view point of global structure of solution sets

Research Project

Project/Area Number	24654037
Research Category	Grant-in-Aid for Challenging Exploratory Research
Allocation Type	Single-year Grants
Research Field	Global analysis
Research Institution	Tohoku University
Principal Investigator	TAKAGI Izumi 東北大学, 理学(系)研究科(研究院), 教授 (40154744)
Project Period (FY)	2012-04-01 – 2014-03-31
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
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.

(5 results)