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New theory for transient dynamics in reaction-diffusion systems allowing collapse of attractors

Research Project

Project/Area Number 24654044
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Global analysis
Research InstitutionRyukoku University

Principal Investigator

MORITA YOSHIHISA  龍谷大学, 理工学部, 教授 (10192783)

Co-Investigator(Kenkyū-buntansha) SUZUKI Kanako  茨城大学, 理学部, 准教授 (10451519)
KUWAMURA Masataka  神戸大学, 人間発達環境学研究科, 教授 (30270333)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords遷移ダイナミクス / 反応拡散系 / 大域アトラクタ / アトラクタの崩壊 / 散逸力学系 / 保存則 / 摂動系 / チューリング的パターン / 反応拡散方程式系 / 無限次元力学系 / 保存則のある反応拡散系 / 大域的アトラクタ / パターン形成 / 応用解析
Outline of Final Research Achievements

We consider reaction-diffusion systems having a global attractor which collapses and turns to be a single stationary state by a perturbation. Although the dynamical structure largely changed by the perturbation, there is a perturbed orbit close to the unperturbed one during a transient time. In a specific reaction-diffusion system with conservation law we show for the perturbed system that a Turing-like wave takes place and it changes to a single spike, then the pattern finally collapses. The perturbed system has no longer steady state solutions which induce a Turing type instability. Nonetheless in the transient dynamics such a Turing-like pattern can be shown.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (22 results)

All 2015 2014 2013 2012

All Journal Article (6 results) (of which Peer Reviewed: 6 results,  Open Access: 2 results,  Acknowledgement Compliant: 1 results) Presentation (15 results) (of which Invited: 15 results) Book (1 results)

  • [Journal Article] Spectral comparison and gradient-like property2015

    • Author(s)
      Chao-Nien Chen, Shuichi Jimbo, and Yoshihisa Morita
    • Journal Title

      Nonlinearity

      Volume: 28 Issue: 4 Pages: 1003-1016

    • DOI

      10.1088/0951-7715/28/4/1003

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Stability of coexisting equilibrium of prey-predator systems with dormancy of predators2014

    • Author(s)
      M. Kuwamura
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 57 Pages: 339-350

    • NAID

      130004678002

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Planar standing wavefronts in the FitzHugh-Nagumo equations2014

    • Author(s)
      C.-N. Chen, S.-Y. Kung, and Y. Morita
    • Journal Title

      SIAM Math. Anal.

      Volume: 46 Issue: 1 Pages: 657-690

    • DOI

      10.1137/130907793

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lyapunov function and spectrum comparison for a reaction-diffusion system with mass conservation2013

    • Author(s)
      S Jimbo, Y Morita
    • Journal Title

      Journal of Differential Equations

      Volume: Vol.255 Issue: 7 Pages: 1657-1683

    • DOI

      10.1016/j.jde.2013.05.021

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Unstable patterns in reaction-diffusion model of early carcinogenesis2013

    • Author(s)
      Anna Marciniak-Czochra, Grzegorz Karch and Kanako Suzuki
    • Journal Title

      Journal de Mathematiques Pures et Appliquees

      Volume: 99巻 Issue: 5 Pages: 509-543

    • DOI

      10.1016/j.matpur.2012.09.011

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nonplanar traveling waves of a bistable reaction-diffusion equation in the multi-dimensional space2012

    • Author(s)
      Y. Morita
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B35 Pages: 1-8

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Turing instability and spatial patterns to reaction-diffusion equations modeling biological pattern formation2015

    • Author(s)
      K. Suzuki
    • Organizer
      Mini-workshop on Models of Directional Movement and their Analysis
    • Place of Presentation
      Kawai Hall, Tohoku University
    • Year and Date
      2015-03-26 – 2015-03-28
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 変分的構造をもつ反応拡散系と安定性解析2015

    • Author(s)
      森田善久
    • Organizer
      RIMS研究集会「パターン形成と界面ダイナミクスの数理」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-01-06 – 2015-01-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 反応拡散系における保存則とパターン形成2014

    • Author(s)
      森田善久
    • Organizer
      2014年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学瀬田キャンパス
    • Year and Date
      2014-12-18 – 2014-12-20
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Gradient-like property and spectral comparison in a mass-conserved reaction-diffusion system2014

    • Author(s)
      Y. Morita
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Universidad Autonoma de Madrid, Madrid, Spain
    • Year and Date
      2014-07-07 – 2014-07-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Spectral comparison and gradient-like property for some reaction-diffusion systems2013

    • Author(s)
      Y. Morita
    • Organizer
      Czech-Japanese Seminar in Applied Mathematics 2013
    • Place of Presentation
      Meiji University Nakano Campus, Japan
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Spectrum Comparison for Reaction-Diffusion systems2013

    • Author(s)
      Y. Morita
    • Organizer
      Equadiff 13
    • Place of Presentation
      Charles University in Prague, Czech Republic
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Instability and blowup phenomena induced by diffusion in some reaction-diffusion-ODE systems2013

    • Author(s)
      K.Suzuki
    • Organizer
      RIMS Workshop on Mathematical Analysis of Pattern Formation Arising in Nonlinear Phenomena
    • Place of Presentation
      RIMS Kyoto University, Japan
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 非拡散物質を含む反応拡散系を用いてパターン形成を考える2013

    • Author(s)
      鈴木 香奈子
    • Organizer
      2013日本数学会秋季総合分科会 応用数学分科会特別講演
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Standing Wavefronts for the FitzHugh-Nagumo System2012

    • Author(s)
      Y. Morita
    • Organizer
      Swiss-Japanese Seminar
    • Place of Presentation
      Institute of Mathematics of the University of Zurich, Switzerland
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Reaction-diffusion systems with conservation of mass2012

    • Author(s)
      Y. Morita
    • Organizer
      Nonlinear Partial Differential Equations, Dynamical Systems and Their Applications
    • Place of Presentation
      RIMS, Kyoto University, Kyoto, Japan
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Planar standing front waves of the FitzHugh-Nagumo system2012

    • Author(s)
      Y. Morita
    • Organizer
      The 9th AIMS Conference on Dynamical Systems and Differential Equations and Applications
    • Place of Presentation
      Orlando, Florida, USA
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Gradient-like property of a reaction-diffusion system with mass conservation2012

    • Author(s)
      Y. Morita
    • Organizer
      The 9th AIMS Conference on Dynamical Systems and Differential Equations and Applications
    • Place of Presentation
      Orlando, Florida, USA
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Behavior of solutions of some reaction-diffusion equations with autocatalysis property2012

    • Author(s)
      K. Suzuki
    • Organizer
      Swiss-Japanese Seminar
    • Place of Presentation
      Institute of Mathematics of the University of Zurich, Switzerland
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Large time behavior of solutions of some reaction-diffusion equations with Turing instability2012

    • Author(s)
      K. Suzuki
    • Organizer
      Turing Symposium on Morphogenesis
    • Place of Presentation
      Sendai International Center, Sendai, Japan
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Stability of patterns in some reaction-diffusion systems with the diffusion-driven instability2012

    • Author(s)
      K. Suzuki
    • Organizer
      The 9th AIMS Conference on Dynamical Systems and Differential Equations and Applications
    • Place of Presentation
      Orlando, Florida, USA
    • Related Report
      2012 Research-status Report
    • Invited
  • [Book] パターン形成と分岐理論2015

    • Author(s)
      桑村雅隆
    • Total Pages
      209
    • Publisher
      共立出版
    • Related Report
      2014 Annual Research Report

URL: 

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

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