New approach to predict various oscillatory dynamics

• Project/Area Number: 20540116
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Meiji University (2011); Osaka University (2008-2010)
• Principal Investigator: OGAWA Toshiyuki 明治大学, 理工学部, 教授 (80211811)
• Co-Investigator(Renkei-kenkyūsha): KUWAMURA Masataka 神戸大学, 発達科学部, 准教授 (30270333)
• Project Period (FY): 2008 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); 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: ウェーブ不安定化 / 反応拡散系 / 3重退化分岐 / 擬似回転波 / 分岐解析 / 0-1-2モード相互作用 / ウェーブ不定化 / 不変トーラス / 球面対称標準形 / ウェーブ分岐 / 時空間パターン / チューリング不安定 / ホップ分岐 / 球面対称性

Research Abstract

Normal form for a wave instability under SO(2) symmetry is studied to understand oscillatory patterns for 3-component reaction-diffusion equations on a sphere. It turns out that there are rotating and standing waves in the case of lower mode instabilities and stabilities for both solutions are studied. Another possibilities for oscillatory patterns are also discussed. It turns out that 3-component RD system can have 1-2-3 triple modes degeneracy and its normal form was obtained. Normal form analysis shows that there is Hopf bifurcation point from 1-mode stationary solution.

Research Products

• [Journal Article] パターン形成の分岐解析(I) (2012)
  • Author(s): 小川知之
  • Journal Title: 応用数理 Volume: 22(1) Pages: 45-50
• [Journal Article] Stability and bifurcation of nonconstant solutions to a reaction-diffusion system with conservation of mass (2010)
  • Author(s): Y. Morita and T. Ogawa
  • Journal Title: Nonlinearity Volume: 23 Pages: 1387-1411
  • Peer Reviewed
• [Journal Article] Stability and bifurcation of nonconstant solutions to a reaction-diffusion system with conservation of mass (2010)
  • Author(s): Y.Morita, T.Ogawa
  • Journal Title: Nonlinearity 23 Pages: 1387-1411
  • Peer Reviewed
• [Journal Article] A minimal model of prey-predator system with dormancy of predators and the paradox of enrichment (2009)
  • Author(s): M. Kuwamura, T. Nakazawa and T. Ogawa
  • Journal Title: J. Math. Biol Volume: 58 Pages: 459-479
  • Peer Reviewed
• [Journal Article] Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions (2009)
  • Author(s): T. Ogawa and T. Okuda
  • Journal Title: Discrete and Continuous Dynamical Systems-A Volume: 25(1) Pages: 273-297
  • Peer Reviewed
• [Journal Article] A minimal model of prey-predator system with dormancy of predators and the paradox of enrichment (2009)
  • Author(s): M.Kuwamura, T.Nakazawa, T.Ogawa
  • Journal Title: J.Math.Biol. 58 Pages: 459-479
  • Peer Reviewed
• [Journal Article] Bifurcation analysis to Swift-Hohenberg equation with Steklov type boundary conditions (2009)
  • Author(s): T.Ogawa, T.Okuda
  • Journal Title: Discrete and Continuous Dynamical Systems-A 25(1) Pages: 273-297
  • Peer Reviewed
• [Journal Article] A minimal model of prey-predator system with dormancyof predators and the paradox of enrichment (2009)
  • Author(s): T. Ogawa, et al.
  • Journal Title: J. Hath. Biol. 58 Pages: 459-479
  • Peer Reviewed
• [Journal Article] Selection principle for various modes of spatially non-uniform electrochemical oscillations (2008)
  • Author(s): S. Fukushima, S. Nakanishi, Y. Nakato and T. Ogawa
  • Journal Title: J. Chemical Physics Volume: 128 Pages: 14714-14714
  • Peer Reviewed
• [Journal Article] Bifurcation analysis to Swift-Hohenberg equationwith. Steklov type boundary conditions
  • Author(s): T. Ogawa., et al.
  • Journal Title: Discrete and Continuous Dynamical System (掲載予定)
  • Peer Reviewed
• [Presentation] 反応拡散系における3重臨界点とそのまわりでのダイナミクス (2011)
  • Author(s): 奥田孝志、小川知之
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-30
• [Presentation] Triply degenerate interactions in 3-component reaction-diffusion system (2011)
  • Author(s): 小川知之
  • Organizer: One Forum Two Cities : Aspect of Nonlinear PDEs
  • Place of Presentation: 国立台湾大学
  • Year and Date: 2011-08-29
• [Presentation] Triple degeneracy on 3-component RD system (2010)
  • Author(s): 小川知之
  • Organizer: Reaction-Diffusion Systems : Experiments, Modeling and Analysis
  • Place of Presentation: パリ南大学(フランス)
  • Year and Date: 2010-10-21
• [Presentation] Triple degeneracy on 3-component RD system (2010)
  • Author(s): T.Ogawa
  • Organizer: Reaction-Diffusion Systems : Experiments, Modeling, and Analysis
  • Place of Presentation: パリ南大学,フランス
  • Year and Date: 2010-10-21
• [Presentation] Rotating and standing waves on sphere (2010)
  • Author(s): 小川知之
  • Organizer: AIMS International Conference on Dynamical Systems
  • Place of Presentation: ドレスデン工科大学(ドイツ)
  • Year and Date: 2010-05-27
• [Presentation] O(3)対称な反応拡散系でのウェーブ分岐 (2009)
  • Author(s): 小川知之
  • Organizer: 日本数学会2009年度秋季総合分科会
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-27
• [Presentation] 0(3)対称な反応拡散系でのウェーブ分岐 (2009)
  • Author(s): 小川知之
  • Organizer: 日本数学会2009年度秋季総合分科会
  • Place of Presentation: 大阪大学豊中キャンパス
  • Year and Date: 2009-09-27
• [Presentation] 0(3)対称な反応拡散系でのウェーブ分岐 (2009)
  • Author(s): 小川知之
  • Organizer: 日本数学会2009年度秋季総合分科会
  • Place of Presentation: 大阪大学
  • Year and Date: 2009-09-27
• [Presentation] 球面上の反応拡散系におけるウェーブ分岐 (2008)
  • Author(s): 小川 知之, 他
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学理工学部
  • Year and Date: 2008-12-16
• [Presentation] Quasi rotating waves to reaction-diffusion system (2008)
  • Author(s): 小川知之
  • Organizer: Singularities arising in Nonlinear Problems 2008
  • Place of Presentation: 京都関西セミナーハウス
  • Year and Date: 2008-12-02
• [Presentation] Quasi rotating waves to reaction-diffusion system (2008)
  • Author(s): 小川 知之
  • Organizer: 研究集会 SNP (Singularities arising in Nonlinear Problems)2008
  • Place of Presentation: 京都関酉セミナーハウス
  • Year and Date: 2008-12-02
• [Presentation] Wave Bifurcation in Coupled Oscillator (2008)
  • Author(s): 小川知之
  • Organizer: International workshop on collective behaviors in bio-and bio-related systems
  • Place of Presentation: 北海道大学電子科学研究所
  • Year and Date: 2008-09-03
• [Presentation] Wave Bifurcation in coupled oscillator (2008)
  • Author(s): 小川 知之
  • Organizer: Intenational workshop on collectivebehaviors in bio- and bio-relatedsystems
  • Place of Presentation: 北海道大学電子科学研究所
  • Year and Date: 2008-09-03
• [Book] 非線形現象と微分方程式パターンダイナミクスの分岐解析 (2010)
  • Author(s): 小川知之
  • Total Pages: 100
  • Publisher: サイエンス社
• [Book] 非線形現象と微分方程式 パターンダイナミクスの分岐解析 (2010)
  • Author(s): 小川知之
  • Total Pages: 100
  • Publisher: サイエンス社