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Investigation of Diverse Bifurcation Structures in Differential Dynamical Systems

Research Project

Project/Area Number 25400168
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionKyoto University (2014-2016)
Hiroshima University (2013)

Principal Investigator

Yagasaki Kazuyuki  京都大学, 情報学研究科, 教授 (40200472)

Co-Investigator(Kenkyū-buntansha) 柴山 允瑠  京都大学, 情報学研究科, 准教授 (40467444)
伊藤 秀一  金沢大学, 数物科学系, 教授 (90159905)
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords力学系 / 偏微分方程式系 / 不規則摂動系 / 周期摂動系 / 区分的に滑らかな系 / 分岐 / カオス / 非可積分性 / 微分方程式 / 反転可能系
Outline of Final Research Achievements

Dynamical systems described by ordinary and partial differential equations were considered and complicated behaviors such as bifurcation structures occurring in these systems were theoretically investigated. Especially, bifurcations and stability of solitary waves in partial differential equations, unique existence and bifurcations of radial symmetric, positive solutions in elliptic partial differential equations, control of microcantilevers in atomic force microscopy, nonintegrability of general differential equations, and chaos in periodic perturbations of conservative systems and random perturbed systems were discussed. Appropriate numerical analyses and simulations were also carried out to demonstrate these theoretical results numerically and graphically.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (48 results)

All 2017 2016 2015 2014 2013

All Journal Article (9 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Acknowledgement Compliant: 2 results,  Open Access: 2 results) Presentation (39 results) (of which Int'l Joint Research: 6 results,  Invited: 15 results)

  • [Journal Article] Rough external feedback control of microcantilevers in atomic force microscopy2017

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      Nonlinear Dynamics

      Volume: 87 Issue: 4 Pages: 2335-2343

    • DOI

      10.1007/s11071-016-3193-3

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Nonintegrability of dynamical systems with homo- and heteroclinic orbits2017

    • Author(s)
      Kazuyuki Yagasaki, Shogo Yamanaka
    • Journal Title

      Journal of Differential Equations

      Volume: 263 Issue: 2 Pages: 1009-1027

    • DOI

      10.1016/j.jde.2017.03.006

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Periodic solutions of a perscribed-energy problem for a singular Hamiltonian system2017

    • Author(s)
      M. Shibayama
    • Journal Title

      Discrete and Continuous Dynamical Systems A

      Volume: 37 Issue: 5 Pages: 2705-2715

    • DOI

      10.3934/dcds.2017116

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some remarks on integrability and normal forms for vector fields2016

    • Author(s)
      Hidekazu Ito
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B57 Pages: 249-264

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Three topologically nontrivial choreographic motions of three bodies2016

    • Author(s)
      Milovan Suvakov, Mitsuru Shibayama
    • Journal Title

      Celestial Mechanics and Dynamical Astronomy

      Volume: 124 Issue: 2 Pages: 155-162

    • DOI

      10.1007/s10569-015-9657-9

    • NAID

      120006601520

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Chaos in randomly perturbed dynamical systems2015

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1942 Pages: 98-104

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] Analytic and algebraic conditions for bifurcations of homoclinic orbits in reversible systems2014

    • Author(s)
      Kazuyuki Yagasaki
    • Journal Title

      Advanced Studies in Pure Mathematics: Nonlinear Dynamics in Partial Differential Equations

      Volume: 64

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Variational proof of the existence of the super-eight orbit in the four-body problem2014

    • Author(s)
      Mitsuru Shibayama
    • Journal Title

      Archive for Rational Mechanics and Analysis

      Volume: 未定

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Minimax approach to the n-body problem2014

    • Author(s)
      Mitsuru Shibayama
    • Journal Title

      Advanced Studies in Pure Mathematics: Nonlinear Dynamics in Partial Differential Equations

      Volume: 64

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] 無限次元Hamilton系における定常解の分岐と非線形Schrodinger方程式への応用2017

    • Author(s)
      矢ヶ崎一幸,山添祥太郎
    • Organizer
      日本数学会2017年度年会
    • Place of Presentation
      首都大学東京(東京都・八王子市)
    • Year and Date
      2017-03-24
    • Related Report
      2016 Annual Research Report
  • [Presentation] Non-integrability of the restricted n-body problem2017

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      天体力学N体力学研究会
    • Place of Presentation
      東京工業大学(東京都・目黒区)
    • Year and Date
      2017-03-23
    • Related Report
      2016 Annual Research Report
  • [Presentation] Non-integrability of the restricted n-body problem2017

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      第6回「ハミルトン系とその周辺」研究集会
    • Place of Presentation
      京都大学(京都府・京都市)
    • Year and Date
      2017-03-10
    • Related Report
      2016 Annual Research Report
  • [Presentation] Normal form theory from the viewpoint of integrability near elliptic equilibria2017

    • Author(s)
      Hidekazu Ito
    • Organizer
      第6回「ハミルトン系とその周辺」研究集会
    • Place of Presentation
      京都大学(京都府・京都市)
    • Year and Date
      2017-03-10
    • Related Report
      2016 Annual Research Report
  • [Presentation] 連立非線形Schrodinger方程式における孤立波解のピッチフォーク分岐と線形安定性2016

    • Author(s)
      矢ヶ崎一幸,山添祥太郎
    • Organizer
      日本数学会2016年度秋季総合分科会
    • Place of Presentation
      関西大学(大阪府・吹田市)
    • Year and Date
      2016-09-17
    • Related Report
      2016 Annual Research Report
  • [Presentation] 周期的な摂動を受ける保存系のヘテロクリニック挙動2016

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2016年度秋季総合分科会
    • Place of Presentation
      関西大学(大阪府・吹田市)
    • Year and Date
      2016-09-17
    • Related Report
      2016 Annual Research Report
  • [Presentation] ホモ/ヘテロクリニック軌道を有する一般的な微分方程式系の非可積分性2016

    • Author(s)
      山中祥五,矢ヶ崎一幸
    • Organizer
      日本数学会2016年度秋季総合分科会
    • Place of Presentation
      関西大学(大阪府・吹田市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Annual Research Report
  • [Presentation] Melnikov processes and chaos in randomly perturbed dynamical systems2016

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando (USA)
    • Year and Date
      2016-07-04
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Periodic solutions of a prescribed-energy problem for a singular Hamiltonian system2016

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando (USA)
    • Year and Date
      2016-07-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Melnikov Processes and Chaos in Randomly Perturbed Dynamical Systems2016

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Orlando (USA)
    • Year and Date
      2016-07-01
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A perturbed Kepler problem in which there are no periodic solutions,2016

    • Author(s)
      柴山允瑠
    • Organizer
      天体力学N体力学研究会
    • Place of Presentation
      豊橋技術科学大学(愛知県・豊橋市)
    • Year and Date
      2016-06-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] Heteroclinic motions in periodic perturbations of conservative systems2016

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      天体力学 N 体力学研究会
    • Place of Presentation
      豊橋技術科学大学(愛知県・豊橋市)
    • Year and Date
      2016-06-11
    • Related Report
      2016 Annual Research Report
  • [Presentation] 周期的な摂動を受ける保存系のヘテロクリニック挙動2016

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS 研究集会「力学系とその関連分野の連携探索」
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2016-06-09
    • Related Report
      2016 Annual Research Report
  • [Presentation] Poincare center problem and normal form theory of vector fields2016

    • Author(s)
      Hidekazu Ito
    • Organizer
      97th Encounter between Mathematicians and Theoretical Physicists "Around Poincare"
    • Place of Presentation
      Strasbourg (France)
    • Year and Date
      2016-06-02
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] ハミルトン系の非可積分性とカオス2016

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      第 30 回計算数理工学フ ォ ーラ ム
    • Place of Presentation
      京都大学 (京都府・京都市)
    • Year and Date
      2016-03-18
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] n体問題の周期軌道の変分解析2016

    • Author(s)
      柴山允瑠
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学 (茨城県・つくば市)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 特異点のブローアップと標準形理論の応用による第一積分の個数の評価2015

    • Author(s)
      柴山允瑠
    • Organizer
      天体力学N体力学研究会
    • Place of Presentation
      SMBCイベントスペース (千葉県・千葉市)
    • Year and Date
      2015-12-25
    • Related Report
      2015 Research-status Report
  • [Presentation] Periodic solutions of a prescribed-energy problem for a singular Hamiltonian system2015

    • Author(s)
      柴山允瑠
    • Organizer
      RIMS研究集会「実領域における常微分方程式の定性的研究」
    • Place of Presentation
      京都大学数理解析研究所 (京都府・京都市)
    • Year and Date
      2015-11-10
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] 原子間力顕微鏡におけるマイクロカンチレバーの概外部フィードバック制御2015

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本応用数理学会2015年度年会
    • Place of Presentation
      金沢大学 (石川県・金沢市)
    • Year and Date
      2015-09-09
    • Related Report
      2015 Research-status Report
  • [Presentation] Integrable and superintegrable vector fields and their normal forms at equilibria2015

    • Author(s)
      Hidekazu Ito
    • Organizer
      Dynamics, Topology and Computations
    • Place of Presentation
      Bedlewo (Poland)
    • Year and Date
      2015-06-17
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Melnikov Processes and Chaos in Randomly Perturbed Dynamical Systems2015

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      2015 NCTS Workshop on Dynamical Systems
    • Place of Presentation
      Taipei (Taiwan)
    • Year and Date
      2015-05-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 楕円型方程式の正値球対称解の存在と分岐2015

    • Author(s)
      矢ヶ崎 一幸
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      明治大学駿河台キャ ンパス (東京都・千代田区)
    • Year and Date
      2015-03-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Existence and uniqueness of positive radial solutions to a class of semilinear elliptic equations in R^d with d≧22015

    • Author(s)
      矢ヶ崎 一幸
    • Organizer
      2014 年度 冬の力学系研究集会
    • Place of Presentation
      日本大学軽井沢研修所 (長野県・軽井沢町)
    • Year and Date
      2015-01-10
    • Related Report
      2014 Research-status Report
  • [Presentation] Analytic and algebraic conditions for bifurcations of homoclinic orbits in reversible systems2014

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      International Conference on Algebraic Methods in Dynamical Systems AMDS 2014
    • Place of Presentation
      Barranquilla (Colombia)
    • Year and Date
      2014-10-07
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Melnikov processes and chaos in randomly perturbed dynamical systems2014

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      2013年度冬の力学系研究集会
    • Place of Presentation
      広島大学東千田キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] Chaos in randomly perturbed dynamical systems2014

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      RIMS研究集会 ランダム力学系理論とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] Melnikov processes and chaos in randomly perturbed dynamical systems2014

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      RIMS Conference/The 6th CREST-SBM International Conference New Directions in Applied Dynamical Systems
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 不規則摂動系におけるカオス2014

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      第10 回日本応用数理学会研究部会連合発表会
    • Place of Presentation
      京都大学吉田キャンパス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 特異点のブローアップによるハミルトン系の可積分性の判定2014

    • Author(s)
      柴山允瑠
    • Organizer
      日本数学会2014年度年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Application of the Subharmonic Melnikov Method to Piecewise Smooth Systems2013

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      SIAM Conference on Applications of Dynamical Systems
    • Place of Presentation
      Snowbird Ski and Summer Resort, Snowbird, Utah, USA
    • Related Report
      2013 Research-status Report
  • [Presentation] Bifurcations from one-parameter families of symmetric periodic orbits in reversible systems2013

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      KAM Theory and Related Topics in Hamiltonian Systems
    • Place of Presentation
      金沢大学サテライト・プラザ
    • Related Report
      2013 Research-status Report
  • [Presentation] u''+λ(-u+u^p)=0 (p>1は実数)のNeumann問題における内部単一ピーク解の分岐ダイアグラム2013

    • Author(s)
      矢ヶ崎一幸
    • Organizer
      日本数学会2013年度秋季総合分科会
    • Place of Presentation
      愛媛大学城北キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] Bifurcation diagram for interior single-peak solutions in a Neumann problem for u"+(u+u^p)=0 with p∈R and p>12013

    • Author(s)
      Kazuyuki Yagasaki
    • Organizer
      RIMS Workshop Progress in Qualitative Theory of Ordinary Differential Equations
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Birkhoff normalization of commuting maps associated with superintegrable systems2013

    • Author(s)
      Hidekazu Ito
    • Organizer
      KAM Theory and Related Topics in Hamiltonian Systems
    • Place of Presentation
      金沢大学サテライト・プラザ
    • Related Report
      2013 Research-status Report
  • [Presentation] Variational proof of the existence of the super-eight orbit in the four-body problem2013

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      KAM Theory and Related Topics in Hamiltonian Systems
    • Place of Presentation
      金沢大学サテライト・プラザ
    • Related Report
      2013 Research-status Report
  • [Presentation] Variational proof of the existence of the super-eight orbit in the four-body problem2013

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      The Asian Mathematical Conference 2013
    • Place of Presentation
      BEXCO, Busan, Korea
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Variational proof of the existence of the super-eight orbit in the four-body problem2013

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      The Sixth International Meeting on Celestial Mechanics
    • Place of Presentation
      The Belletti Park Hotel San Martino al Cimino, Viterbo, Itary
    • Related Report
      2013 Research-status Report
  • [Presentation] 変分法による軌道の探索2013

    • Author(s)
      柴山允瑠
    • Organizer
      第56回自動制御連合講演会
    • Place of Presentation
      新潟大学五十嵐キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] Variational proof of the existence of the super-eight orbit in the four-body problem2013

    • Author(s)
      Mitsuru Shibayama
    • Organizer
      Taiwan-Japan Symposium on Celestial Mechanics and N-Body Dynamics
    • Place of Presentation
      The national Tsing Hua University, Hsinchu city, Taiwan
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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