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

• Project/Area Number: 18740093
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Fukuoka 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: ¥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。

Research Products

• [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)
  • Peer Reviewed
• [Journal Article] Limiting characterization of stationary solutions for a prey-predator model with nonlinear diffusion of fractional type (2009)
  • Author(s): Kousuke Kuto, Yoshio Yamada
  • Journal Title: Differential and Integral Equations 22 Pages: 725-752
  • 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
  • Peer Reviewed
• [Journal Article] Bifurcation branch of stationary solutions for a Lotka Volterra cross?diffusion system in a spatially heterogeneous environment (2009)
  • Author(s): Kousuke Kuto
  • Journal Title: Nonlinear Analysis Series B: Real Worid Applications 10 Pages: 943-965
  • Peer Reviewed
• [Journal Article] Bifurcation phenomena of pattern solution to Mimura?Tsujikawa model in one dimension (2008)
  • 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
  • Peer Reviewed
• [Journal Article] Bifurcation phenomena of pattern solution to Mimura-Tsuiikawa model in one dimension (2008)
  • Author(s): Naoko Kurata
  • Journal Title: GAKUTO International Series, Mathematical Sciences and Applications 29 Pages: 256-278
  • 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
  • Peer Reviewed
• [Journal Article] A Lotka?Volterra cross-diffusion model in spatially heter ogeneous environments (2007)
  • 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
• [Journal Article] A Lotka-Volterra cross-diffusion model in spatially heterogene ous environments (2007)
  • Author(s): Kousuke Kuto
  • Journal Title: 京都大学数理解析研究所講究録 1542 Pages: 41-57
• [Journal Article] Pattern formation for adsorbate-induced phase transition model (2007)
  • 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
  • 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: Advances in Differential Equations Vol.12,No.2 Pages: 145-172
• [Presentation] Limiting charact erization for coexistence states to a Lotka?Volterra model with nonlinear diffusion of fractional type (2008)
  • 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
• [Presentation] Limiting characterization for coexistence states to a Lotka-Volterra model with nonlinear diffusion of fractional ype (2008)
  • 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
• [Presentation] Coexistence problem for a prey-predator model with density-dependence diffusion (2008)
  • Author(s): Kousuke Kuto
  • Organizer: The 5th World Congress of Nonlinear Analysts
  • Place of Presentation: Orlando, Florida
  • Year and Date: 2008-07-03
• [Presentation] Coexistence problem for a prey-predator model with density-dependence diffusion (2008)
  • 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
• [Presentation] Stability of steady-states to the SKT model in a heterogeneousenvironment (2007)
  • 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
• [Presentation] Stability of steady-states to the SKT model in a heterogeneous environment (2007)
  • 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
• [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
• [Presentation] Coexistence steady-states of a Lotka?Volterra cross?diffusion system in spatially heterogeneous environment (2006)
  • 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
• [Remarks]
  • URL: http://www.fit.ac.jp/kuto/
• [Remarks]
  • URL: http://www.fit.ac.jp/kuto/
• [Remarks]
  • URL: http://www.fit.ac.jp/~kuto/