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Reaction Diffusion Dynamics in non-homogeneous media

Research Project

Project/Area Number 20540212
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionHiroshima University

Principal Investigator

SAKAMOTO Kunimoch  Hiroshima University, 大学院・理学研究科, 教授 (40243547)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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 / パターンダイナミク / 非正常分岐現象 / 周期解 / Turing不安定性 / 波動分岐 / 領域境界の曲率 / 曲率の非一様性 / 空間周期解 / 安定性・軌道安定性 / 反応拡散方程式系 / Riemann計量と非一様拡散 / Fokker-Planck方程式 / 非一様場 / 特異極限
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.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (18 results)

All 2010 2009 2008

All Presentation (18 results)

  • [Presentation] Turing instability for three-component systems2010

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      NCTS Workshop on PDE models for Biological Processes
    • Place of Presentation
      Tsing-Hua University(新竹市、台湾)
    • Year and Date
      2010-12-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Turing Instability for Three Component Systems2010

    • Author(s)
      坂元国望
    • Organizer
      NCTS Workshop on PDE Models of Biological Processes
    • Place of Presentation
      Tsing-Hua University(台湾)
    • Year and Date
      2010-12-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stability and Bifurcation of Rotating Waves in Nonlinear Equations2010

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      The 4-th International Conference on Recent Advances in Applied Dynamical Systems
    • Place of Presentation
      Zhejian Normal University(金華市、中華人民共和国)
    • Year and Date
      2010-06-17
    • Related Report
      2010 Final Research Report
  • [Presentation] Stability and Bifrcation of Rotating Waves in Nonlinear Equations2010

    • Author(s)
      坂元国望
    • Organizer
      The Fourth International Conference on Recent Advances in Applied Dynamicsl Systems
    • Place of Presentation
      Zhejiang Normal University(中華人民共和国)(招待講演)
    • Year and Date
      2010-06-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Diffusion systems with interacting flux on the boundary2010

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      8-th AIMS International conference on Dynaimcal Systems, Differential Equations and Applications, Dresden University of Technology
    • Place of Presentation
      Dresden,ドイツ連邦共和国
    • Year and Date
      2010-05-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Diffusion Systems with Interacting Flux on the Boundary2010

    • Author(s)
      坂元国望
    • Organizer
      8-th AIMS International Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Dresden University of Technology(ドイツ)
    • Year and Date
      2010-05-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stability and Bifurcation of Periodic waves in a dispersive system2010

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      日韓協同研究集会(ダイナミカルシステムとその周辺)
    • Place of Presentation
      釜山大学(釜山、韓国)
    • Year and Date
      2010-03-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Stability and Bifurcation of Periodic Waves in a Dispersive System2010

    • Author(s)
      坂元国望
    • Organizer
      日韓共同研究集会「ダイナミカルシステムとその周辺」
    • Place of Presentation
      釜山大学(韓国)
    • Year and Date
      2010-03-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Stability and bifurcation of Periodic Waves in nonlinear equations2010

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      RIMS研究集会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2010-01-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Stability and Bifurcation of Periodic Waves in non-linear equations2010

    • Author(s)
      坂元国望
    • Organizer
      RIMS研究集会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2010-01-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] Stability and Bifurcation of Periodic Waves in a Hamiltonian PDE2009

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      国際研究集会SNP2009
    • Place of Presentation
      関西セミナーハウス(京都市)
    • Year and Date
      2009-11-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Stability and Bifurcation of Periodic Waves in a Hamiltonian PDE2009

    • Author(s)
      坂元国望
    • Organizer
      国際研究集会SNP2009
    • Place of Presentation
      関西セミナーハウス(京都)
    • Year and Date
      2009-11-02
    • Related Report
      2009 Annual Research Report
  • [Presentation] Stability and bifurcation of periodic travelling waves in derivative nonlinear Schroedinger equations2009

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      2nd International Conference on Reaction-Diffusion Systems and Viscosity Solutions
    • Place of Presentation
      Providence University(沙鹿市、台湾)
    • Year and Date
      2009-07-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Stability and bifurcation of periodic travelling waves in derivative nonlinear Schroedinger equations2009

    • Author(s)
      坂元国望
    • Organizer
      2^<nd> International Conference on Reaction-Diffusion Systems and Viscosity Solutions
    • Place of Presentation
      Providence University (台湾)
    • Year and Date
      2009-07-14
    • Related Report
      2009 Annual Research Report
  • [Presentation] 蔵本モデルの定常解-振動数分布の非対称性と特異摂動の観点から-2009

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      京都大学結合系セミナー
    • Place of Presentation
      京都大学
    • Year and Date
      2009-03-18
    • Related Report
      2010 Final Research Report
  • [Presentation] 蔵本モデルの定常解 -振動数分布の非対称性と特異摂動の観点から-2009

    • Author(s)
      坂元国望
    • Organizer
      京都大学 結合系セミナー
    • Place of Presentation
      京都大学理学研究科
    • Year and Date
      2009-03-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] 蔵本モデルにおける特異摂動問題2008

    • Author(s)
      Sakamoto Kunimochi
    • Organizer
      盛岡応用数学小研究集会
    • Place of Presentation
      岩手大学
    • Year and Date
      2008-12-14
    • Related Report
      2010 Final Research Report
  • [Presentation] 蔵本モデルにおける特異摂動問題2008

    • Author(s)
      坂元国望
    • Organizer
      盛岡応用数学小研究集会
    • Place of Presentation
      岩手大学人文社会科学部
    • Year and Date
      2008-12-14
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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