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Study on the structure of solutions for the Lotka?Volterra system with cross?diffusion

Research Project

Project/Area Number 18740093
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionFukuoka Institute of Technology

Principal Investigator

KUTO Kousuke  Fukuoka Institute of Technology, 工学部, 准教授 (40386602)

Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,670,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywords非線形現象 / 反応拡散方程式 / 定常解 / 分岐 / 数理生物学モデル / 相互拡散(cross-diffusion) / ロトカ・ボルテラ系 / 楕円型偏微分方程式 / 共存定常解 / 分数型非線形拡散 / 空間非一様性 / 安定性 / 重定-川崎-寺本モデル
Research Abstract

相互拡散(cross-diffusion)を伴うロトカ・ボルテラ系に対して定常解の大域分岐構造が得られた。捕食生物と餌となる生物の個体数密度がなす時空的ダイナミクスを記述する系においては、それぞれの生物の空間的拡散や捕食に関する相互作用の地域差に応じて、生物が共存する定常解がなす分岐枝が釣り針状に変形し、解が複数個存在することが判明した。また、分数型の相互拡散を伴う系においては、相互拡散項の増大に応じて、共存定常解が2種類のサイズに分類されることが分かった。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (22 results)

All 2009 2008 2007 2006 Other

All Journal Article (11 results) (of which Peer Reviewed: 8 results) Presentation (8 results) Remarks (3 results)

  • [Journal Article] Coexistence problem for a prey- predator model with density-dependent diffusion, Nonlinear Analysis,2009

    • Author(s)
      Kousuke Kuto, Yoshio Yamada,
    • Journal Title

      Series A: Theory, Methods and Applications (Available online)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type2009

    • Author(s)
      Kousuke Kuto, Yoshio Yamada
    • Journal Title

      Differential and Integral Equations 22

      Pages: 725-752

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability and Hopf bifurcation of coexistence steady-states to an SKT model in spatially hete rogeneous environrnent,2009

    • Author(s)
      KousukeKuto
    • Journal Title

      Discreteand Continuous Dynamical Systelns 24

      Pages: 489-509

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation branch of stationary solutions for a Lotka Volterra cross?diffusion system in a spatially heterogeneous environment2009

    • Author(s)
      Kousuke Kuto
    • Journal Title

      Nonlinear Analysis Series B: Real Worid Applications 10

      Pages: 943-965

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation phenomena of pattern solution to Mimura?Tsujikawa model in one dimension2008

    • Author(s)
      Naoko Kurata, Kousuke Kuto, Koichi O saki, Tohru Tsujikawa, Tatsunari Sak urai
    • Journal Title

      GAKUTO International Series, Mathematical Sciences and Applications 29

      Pages: 265-278

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation phenomena of pattern solution to Mimura-Tsuiikawa model in one dimension2008

    • Author(s)
      Naoko Kurata
    • Journal Title

      GAKUTO International Series, Mathematical Sciences and Applications 29

      Pages: 256-278

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A strongly coupled diffusion effect on the stationary solution set of a prey-predator model,2007

    • Author(s)
      Kousuke Kuto
    • Journal Title

      A dvances in Differential Equations 12

      Pages: 145-172

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Lotka?Volterra cross-diffusion model in spatially heter ogeneous environments2007

    • Author(s)
      Kousuke Kuto
    • Journal Title

      京都大学数理解析研究所講究録「現象の数理モデルと発展方程式」 1542

      Pages: 41-57

    • Related Report
      2008 Final Research Report
  • [Journal Article] A Lotka-Volterra cross-diffusion model in spatially heterogene ous environments2007

    • Author(s)
      Kousuke Kuto
    • Journal Title

      京都大学数理解析研究所講究録 1542

      Pages: 41-57

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Pattern formation for adsorbate-induced phase transition model2007

    • Author(s)
      Kousuke Kuto and Tohru Tsujikawa
    • Journal Title

      京都大学数理解析研究所講究録 別冊3

      Pages: 43-58

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A strongly coupled diffusion effect on the stationary solution set of a prey-predator model2007

    • Author(s)
      Kousuke Kuto
    • Journal Title

      Advances in Differential Equations Vol.12,No.2

      Pages: 145-172

    • Related Report
      2006 Annual Research Report
  • [Presentation] Limiting charact erization for coexistence states to a Lotka?Volterra model with nonlinear diffusion of fractional type2008

    • Author(s)
      久藤衡介,山田義雄
    • Organizer
      日本数学会総合分科会関数方程式分科会
    • Place of Presentation
      東京工業大学大岡山キヤンパス
    • Year and Date
      2008-09-25
    • Related Report
      2008 Final Research Report
  • [Presentation] Limiting characterization for coexistence states to a Lotka-Volterra model with nonlinear diffusion of fractional ype2008

    • Author(s)
      久藤衡介
    • Organizer
      日本数学会総合分科会関数方程式分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Coexistence problem for a prey-predator model with density-dependence diffusion2008

    • Author(s)
      Kousuke Kuto
    • Organizer
      The 5th World Congress of Nonlinear Analysts
    • Place of Presentation
      Orlando, Florida
    • Year and Date
      2008-07-03
    • Related Report
      2008 Final Research Report
  • [Presentation] Coexistence problem for a prey-predator model with density-dependence diffusion2008

    • Author(s)
      Kousuke Kuto
    • Organizer
      The 5th World Congress of Nonlinear Analysis
    • Place of Presentation
      Orlando, Hyatt Regency Hotel, Florida
    • Year and Date
      2008-07-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] Stability of steady-states to the SKT model in a heterogeneousenvironment2007

    • Author(s)
      久藤衡介
    • Organizer
      日本数学会総合分科会関数方程式分科会
    • Place of Presentation
      東北大学川内北キャンパス
    • Year and Date
      2007-09-24
    • Related Report
      2008 Final Research Report
  • [Presentation] Stability of steady-states to the SKT model in a heterogeneous environment2007

    • Author(s)
      久藤 衡介
    • Organizer
      日本数学会総合分科会(関数方程式分科会)
    • Place of Presentation
      東北大学川内北キャンパス
    • Year and Date
      2007-09-24
    • Related Report
      2007 Annual Research Report
  • [Presentation] 空間非一様な環境下でのLotka-Volterra交差拡散系に対する定常解2006

    • Author(s)
      久藤衡介
    • Organizer
      日本数学会総合分科会関数方程式分科会
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2006-09-20
    • Related Report
      2008 Final Research Report
  • [Presentation] Coexistence steady-states of a Lotka?Volterra cross?diffusion system in spatially heterogeneous environment2006

    • Author(s)
      久藤衡介
    • Organizer
      第16回日本数理生物学会大会
    • Place of Presentation
      九州大学箱崎キヤンパス
    • Year and Date
      2006-09-18
    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.fit.ac.jp/kuto/

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://www.fit.ac.jp/kuto/

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.fit.ac.jp/~kuto/

    • Related Report
      2007 Annual Research Report

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

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