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Hamiltonian structure in the pattern selection problems of dissipative systems

Research Project

Project/Area Number 18540120
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKobe University

Principal Investigator

KUWAMURA Masataka  Kobe University, 人間発達環境学研究科, 准教授 (30270333)

Co-Investigator(Kenkyū-buntansha) EI Shin-ichiro  九州大学, 数理学研究院, 教授 (30201362)
OGAWA Toshiyuki  大阪大学, 基礎工学研究科, 准教授 (80211811)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Keywords散逸系 / ハミルトン系 / prey-predator / カオス / mixed-mode振動 / ハミルトン構造 / 波数選択 / チューリングパターン / 周期解 / 時間遅れ / パターン
Research Abstract

We studied the gradient/skew-gradient structure that enables us to apply the Hamiltonian formalism for studying the stability of stationary solutions in reaction-diffusion systems in various pattern formation problems. Moreover, we studied the stabilizing effect of dormancy of predators on the population dynamics of prey-predator systems.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (29 results)

All 2009 2008 2007 2006 Other

All Journal Article (17 results) (of which Peer Reviewed: 13 results) Presentation (10 results) Remarks (2 results)

  • [Journal Article] Mixed-mode oscillations and chaos in a prey-predator system with dormancy of predators2009

    • Author(s)
      M. Kuwamura, H. Chiba
    • Journal Title

      Chaos vol.19

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] minimum model of prey-predator system with dormancy of predators and the paradox of enrichment2009

    • Author(s)
      M. Kuwamura, T. Nakazawa, T. Ogawa
    • Journal Title

      Journal of Mathematical Biology vol.58

      Pages: 459-479

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A minimum model of prey-predator system with dormancy of predators and the paradox of enrichment2009

    • Author(s)
      M.Kuwamura, T.Nakazawa, T.Ogawa
    • Journal Title

      J.Math.Biol. 58

      Pages: 459-479

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Mixed-mode oscillations and chaos in a prey-predator system with dorm ancy of predators2009

    • Author(s)
      M.Kuwamura, H.Chiba
    • Journal Title

      Chaos 19

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A minimum model of prey-predator systemwith dormancy of predators and the paraparadoxof enrichment2009

    • Author(s)
      M.Kuwamura, T.Nakazawa and T.Ogawa
    • Journal Title

      Journal of Mathematical Biology vol.58

      Pages: 459-479

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Deviation from the predicted wave number in a mode selection problem for the Turing patterns2008

    • Author(s)
      M. Kuwamura
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics vol.25

      Pages: 281-303

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Deviation from the predicted wavenumber in a mode selection problem for theTuring patterns2008

    • Author(s)
      M.Kuwamura
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics vol.25

      Pages: 281-303

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Deviation from the predicted wavenumber in a mode selection problem for the Turing patterns2008

    • Author(s)
      Masataka Kuwamura
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 25

      Pages: 281303-281303

    • NAID

      10023986000

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Hamiltonian formalism in reaction-diffusion systems2007

    • Author(s)
      M. Kuwamura
    • Journal Title

      Advanced Studies in Pure Mathematics vol.47

      Pages: 635-646

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] TheHamiltonian formalism in reaction diffusion systems2007

    • Author(s)
      M.Kuwamura
    • Journal Title

      Advanced Studies in Pure Mathematics, vol.47,

      Pages: 635-646

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] The Hamiltonian formalism in reaction-diffusion systems2007

    • Author(s)
      Masataka Kuwamura
    • Journal Title

      Advanced Studies in Pure Mathematics 47

      Pages: 635-646

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems2006

    • Author(s)
      M. Kuwamura, E. Yanagida
    • Journal Title

      Journal of Differential Equations vol.230

      Pages: 446-464

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems2006

    • Author(s)
      M.Kuwamura and E.Yanagida
    • Journal Title

      Journal of Differential Equations vol.230,

      Pages: 446-464

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems2006

    • Author(s)
      Masataka Kuwamura
    • Journal Title

      Journal of Differential Equations 230

      Pages: 446-464

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Bursting oscillations and chaos in a prey-predator system with dormancy of predators

    • Author(s)
      桑村雅隆, 千葉逸人
    • Journal Title

      京都大学数理解析研究所講究録(掲載決定) (未定)

    • Related Report
      2008 Annual Research Report
  • [Journal Article] 時間遅れを考慮したCO_2排出戦略

    • Author(s)
      本田卓也、細田一史、桑村雅隆、高橋大輔
    • Journal Title

      京都大学数理解析研究所講究録 (掲載決定)

    • Related Report
      2007 Annual Research Report
  • [Journal Article] 捕食者の休眠を考慮した捕食者-非食者モデル : 富栄養化の逆説の解消に向けて

    • Author(s)
      仲澤剛史
    • Journal Title

      京都大学数理解析研究所講究録 (掲載決定)

    • Related Report
      2006 Annual Research Report
  • [Presentation] 捕食者の休眠を伴うprey-predator系について2009

    • Author(s)
      桑村雅隆
    • Organizer
      日本数学会2009年度秋期総合分科会応用数学分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
    • Related Report
      2009 Final Research Report
  • [Presentation] 捕食者の休眠を伴う prey-predator 系について2009

    • Author(s)
      桑村雅隆
    • Organizer
      日本数学会2009年度秋期総合分科会応用数学分科会
    • Place of Presentation
      大阪大学(大阪府)
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Bursting oscillations and chaos in a prey-predator system with dormancy of predators2009

    • Author(s)
      桑村雅隆, 千葉逸人
    • Organizer
      第5回生物数学の理論とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] Mathematical modeling and experiments for the proliferataion and differentialion of Drosophila intesitinal stem cells2008

    • Author(s)
      Masataka Kuwamura, Kousuke Maeda, Adachi-Yamada Takashi
    • Organizer
      The second China-Japan Colloquium of Mathematical Biology
    • Place of Presentation
      岡山大学
    • Year and Date
      2008-08-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] T. Adachi-Yamada, Mathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells2008

    • Author(s)
      M. Kuwamura, K. Maeda
    • Organizer
      The second China-Japan Colloquim of Mathematical Biology
    • Place of Presentation
      岡山大学
    • Related Report
      2009 Final Research Report
  • [Presentation] T.Adachi-Yamada, Mathematical modeling and experimentsfor the proliferation and differentiation of Drosophila intestinal stem cells2008

    • Author(s)
      M.Kuwamura, K.Maeda
    • Organizer
      The second China-Japan Colloquim of Mathematical Biology
    • Place of Presentation
      岡山大学
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] 時間遅れを考慮したCO_2排出戦略2007

    • Author(s)
      本田卓也、細田一史、桑村雅隆、高橋大輔
    • Organizer
      新しい生物数学の研究交流プロジェクト
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-08-31
    • Related Report
      2007 Annual Research Report
  • [Presentation] 高橋大輔時間遅れを考慮したCO2排出規制戦略2007

    • Author(s)
      本田卓也, 細田一史, 桑村雅隆
    • Organizer
      新しい生物数学の研究交流プロジェクト
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2009 Final Research Report
  • [Presentation] 時間遅れを考慮したCO2 排出規制戦略2007

    • Author(s)
      本田卓也, 細田一史, 桑村雅隆, 高橋大輔
    • Organizer
      新しい生物数学の研究交流プロジェクト
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] A mathematical model of prey-predator system with dormancy of predator2006

    • Author(s)
      仲澤剛史, 桑村雅隆, 霜田めぐみ
    • Organizer
      新しい生物数学の研究交流プロジェクト
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Remarks]

    • URL

      http://wwwmain.h.kobe-u.ac.jp/~kuwamura/kuwaj.html

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://wwwmain.h.kobe-u.ac.jp/~kuwamura/kuwaj.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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