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2013 Fiscal Year Final Research Report

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

Research Project

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Project/Area Number 24654037
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionTohoku 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.

  • Research Products

    (5 results)

All 2013 2012 Other

All Presentation (4 results) Remarks (1 results)

  • [Presentation] Point-condensation phenomenon in a reaction-diffusion system : geometry of domain vs. heterogeneity of media2013

    • Author(s)
      Izumi Takagi
    • Organizer
      Pacific Rim Conference on Mathematics 2013
    • Place of Presentation
      Sapporo Convention Center, 札幌市
    • Year and Date
      2013-07-03
  • [Presentation] Dynamics of a boundary-spike solution on an invariant manifold to a semilinear parabolic equation2013

    • Author(s)
      Izumi Takagi
    • Organizer
      Asian Mathematical Conference
    • Place of Presentation
      BEXCO,Busan,Korea
    • Year and Date
      2013-07-01
  • [Presentation] On the movement of a boundary-spike solution of a semilinear parabolic equation2013

    • Author(s)
      Izumi Takagi
    • Organizer
      Applied and Computational Mathematics
    • Place of Presentation
      University of California,Irvine,USA
    • Year and Date
      2013-03-11
  • [Presentation] What Turing anticipated in 1952-一Impacts on mathematics2012

    • Author(s)
      Izumi Takagi, Eiji Yanagida
    • Organizer
      Turing Symposium on Morphogenesis
    • Place of Presentation
      仙台市国際センター, 仙台市
    • Year and Date
      2012-08-27
  • [Remarks]

    • URL

      http://morpho.sci.tohoku.ac.jp/~morpho/

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Published: 2015-06-25  

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