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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 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
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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 / 定常解の分岐 / 特異摂動解 / 大域的構造
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.

Report

(3 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • Research Products

    (11 results)

All 2013 2012 Other

All Presentation (8 results) (of which Invited: 3 results) Remarks (3 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
    • Related Report
      2013 Final Research Report
  • [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
    • Related Report
      2013 Final Research Report
  • [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
    • Related Report
      2013 Final Research Report
  • [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, Japan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [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
    • Related Report
      2013 Final Research Report
  • [Presentation] What Turing anticipated in 1952--Impacts on mathematics

    • Author(s)
      高木 泉,柳田 英二
    • Organizer
      Turing Symposium on Morphogenesis--Mathematical Approaches Sixty Years after Alan Turing--
    • Place of Presentation
      仙台
    • Related Report
      2012 Research-status Report
  • [Presentation] Movement of a solution having a single spike on the boundary of a semilinear parabolic equation

    • Author(s)
      高木 泉
    • Organizer
      American Mathematical Society Southeastern Section Meeting
    • Place of Presentation
      New Orleans, 米国
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] A Versatile Pattern Generator---from a Mathematical Point of View---

    • Author(s)
      高木 泉
    • Organizer
      Advanced Mathematical Sciences D "Pattern Formation: Legacy of Alan Turing"
    • Place of Presentation
      川崎
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks]

    • URL

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

    • Related Report
      2013 Final Research Report
  • [Remarks] 生物の形づくりの数理

    • URL

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

    • Related Report
      2013 Annual Research Report
  • [Remarks] 生物の形づくりの数理

    • URL

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

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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