A bifurcationtheory of infinitedimensional dynamical systems and its applications to coupled oscillators

• Project/Area Number: 22740069
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kyushu University
• Principal Investigator: CHIBA Hayato 九州大学, マス・フォア・インダストリ研究所, 助教 (70571793)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 力学系 / 解析学 / 蔵本モデル / 無限次元力学系 / スペクトル理論

Research Abstract

A system of coupled oscillators called the Kuramoto model, which describes synchronization phenomena, has been investigated. I have established a new spectral theory of linear operators based on a Gelfand triplet, and it is applied to prove the Kuramoto conjecture on a bifurcation structure ofthe Kuramoto model. It is revealed that a synchronization occurs if the couplingstrength is sufficiently large

Research Products

• [Journal Article] Continuous limit of the moments system for the globally coupled phase oscillators (2013)
  • Author(s): H.Chiba
  • Journal Title: Discret. Contin. Dyn. S.-A Volume: Vol.33 Pages: 1891-1903
• [Journal Article] Continuous limit of the moments system for the globally coupled phase oscillators, (2013)
  • Author(s): H.Chiba
  • Journal Title: Discrete and Continuous Dynamical Systems Series A Volume: 33 Issue: 5 Pages: 1891-1903
  • DOI: 10.3934/dcds.2013.33.1891
  • Peer Reviewed
• [Journal Article] Center manifold reduction for a large population of globally coupled phase oscillators (2011)
  • Author(s): H.Chiba, I.Nishikawa
  • Journal Title: Chaos Volume: 21 Pages: 43103-43103
  • NAID: 120005133101
  • URL: http://dx.doi.org/10.1063/1.3647317
• [Journal Article] Center manifold reduction for a large population of globally coupled phase oscillators (2011)
  • Author(s): Hayato Chiba, et al
  • Journal Title: Chaos Volume: 21 Issue: 4 Pages: 43103-43103
  • DOI: 10.1063/1.3647317
  • NAID: 120005133101
  • Peer Reviewed
• [Journal Article] Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points (2011)
  • Author(s): Hayato Chiba
  • Journal Title: Journal of Differential Equations Volume: 250 Pages: 112-160
  • Peer Reviewed
• [Journal Article] Linear stability of the incoherent solution and the transition formula for the Kuramoto-Daido model (2010)
  • Author(s): H.Chiba
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B21
• [Journal Article] Linear stability of the incoherent solution and the transition formula for the Kuramoto-Daido model (2010)
  • Author(s): Hayato Chiba
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B21 Pages: 109-128
  • Peer Reviewed
• [Presentation] Gelfand の3 つ組を用いた線形作用素のスペクトル理論と,その結合振動子系のダイナミクスへの応用 (2013)
  • Author(s): 千葉逸人
  • Organizer: 日本数学会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-21
• [Presentation] A spectral theory of linear operators on a Gelfand triplet and its application to the Kuramoto model (2012)
  • Author(s): 千葉逸人
  • Organizer: 微分方程式の総合的研究
  • Place of Presentation: 京都大学
  • Year and Date: 2012-12-15
• [Presentation] 一般化スペクトル理論とその結合振動子系のダイナミクス への応用 (2012)
  • Author(s): 千葉逸人
  • Organizer: 数学会北海道支部会
  • Place of Presentation: 北海道大学
  • Year and Date: 2012-12-06
• [Presentation] A spectral theory of linear operators on Gelfand triplets and its applications to infinite dimensional dynamical systems (2012)
  • Author(s): H.Chiba
  • Organizer: Dynamical Systems: 100 years after Poincare
  • Place of Presentation: Gijon, Spain.
  • Year and Date: 2012-09-06
• [Presentation] A spectral theory of linear operators on Gelfand triplets and its applications (2012)
  • Author(s): H.Chiba
  • Organizer: 2012 NCTS Workshop on Dynamical Systems
  • Place of Presentation: National Center of Theoretical Sciences , 台湾
  • Year and Date: 2012-05-16
• [Presentation] Synchronization -A bifurcation theory of infinite dimensional dynamical systems (2012)
  • Author(s): H.Chiba
  • Organizer: GCOE International Symposium on Weaving Science Web beyond Particle-Matter Hierarchy
  • Place of Presentation: 東北大学
  • Year and Date: 2012-02-20
• [Presentation] A spectral theory of linear operators on Gelfand triplets (2011)
  • Author(s): H.Chiba
  • Organizer: Emerging Topics on Differential Equations and their Applications
  • Place of Presentation: Nankai Univ., 天津.
  • Year and Date: 2011-12-05
• [Presentation] A spectral theory of linear operators on Gelfand triplets (2011)
  • Author(s): Hayato Chiba
  • Organizer: Emerging Topics on Differential Equations and their Applications
  • Place of Presentation: 天津、中国(招待講演)
  • Year and Date: 2011-12-05
• [Presentation] A spectral theory on Gelfand triplets (2011)
  • Author(s): H.Chiba
  • Organizer: Workshop on Nonlinear Partial Differential Equations
  • Place of Presentation: Normal Univ.上海
  • Year and Date: 2011-11-04
• [Presentation] Bifurcation theory of the infinite-dimensional Kuramoto model (2010)
  • Author(s): H.Chiba
  • Organizer: Symmetry Plus Integrability 2010
  • Place of Presentation: South Padre Island, Texas
  • Year and Date: 2010-06-13
• [Presentation] Bifurcation theory of the infinite-dimensional Kuramoto model (2010)
  • Author(s): Hayato Chiba
  • Organizer: Symmetry Plus Integrability 2010
  • Place of Presentation: USA, Texas(招待講演)
  • Year and Date: 2010-06-13
• [Presentation] Gelfandの3つ組を用いた線形作用素のスペクトル理論と, その結合振動子系のダイナミクスへの応用
  • Author(s): 千葉逸人
  • Organizer: 日本数学会
  • Place of Presentation: 京都大学
  • Invited
• [Presentation] A spectral theory of linear operators on Gelfand triplets and its applications to infinite dimensional dynamical systems
  • Author(s): H.Chiba
  • Organizer: Dynamical Systems: 100 years after Poincare
  • Place of Presentation: Spain
  • Invited
• [Remarks]
  • URL: http://www2.math.kyushu-u.ac.jp/~chiba/