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力学系:理論と応用の新展開

Research Project

Project/Area Number 18H03671
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Review Section Medium-sized Section 12:Analysis, applied mathematics, and related fields
Research InstitutionKyoto University

Principal Investigator

國府 寛司  京都大学, 理学研究科, 教授 (50202057)

Co-Investigator(Kenkyū-buntansha) 角 大輝  京都大学, 人間・環境学研究科, 教授 (40313324)
荒井 迅  中部大学, 創発学術院, 教授 (80362432)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Granted (Fiscal Year 2022)
Budget Amount *help
¥43,810,000 (Direct Cost: ¥33,700,000、Indirect Cost: ¥10,110,000)
Fiscal Year 2022: ¥8,970,000 (Direct Cost: ¥6,900,000、Indirect Cost: ¥2,070,000)
Fiscal Year 2021: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Fiscal Year 2020: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2019: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000)
Fiscal Year 2018: ¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Keywords力学系 / 分岐 / 大域的構造 / ランダム / 時系列
Outline of Annual Research Achievements

研究計画に従い,2019年度から2021年度(2019年度の繰越分と事故繰越分)に行った研究は以下のとおりである:
課題(LDF=Large Degrees of Freedom systems)では、國府は海外共同研究者 K. Mischaikow らと遺伝子制御ネットワークの1つの数理モデル化である switching system と呼ばれる区分的線型の結合ODE系のダイナミクスの研究を進めた。また分担者の荒井は、高次元力学系の構造を位相力学系と複素力学系の双方の視点から解析する研究を進め、特にエノン写像のパラメータ空間の位相的な構造についての新しい結果を得た。
課題(RSV=Random and Set-Valued dynamical systems)では分担者の角はランダム複素力学系の研究を行った。特に、独立同分布とは限らない、マルコフ的ランダム力学系の基礎理論を構築し、その安定性などについて考察し、論文にまとめて発表した。
課題(HPS=Hybrid and Piecewise Smooth systems)では、國府は岡本耕太・青井伸也らと共同で歩行・走行遷移に関係するハイブリッド力学系の分岐の解析を行った。
課題(DTD=Dynamical Time-series and Data)では、國府は大学院生の原誠人と共同で、リザバー計算と呼ばれる機械学習手法を用いて、力学系の時系列データからリザバー計算により元の力学系の情報が復元される数学的機構についての数値的研究を行った。特に力学系を学習したリザバー計算システムが、学習対象の力学系の情報を超えて、学習データに含まれない相空間構造や分岐の情報までも復元することを、ロジスティック写像と呼ばれるカオス力学系の場合に精密に研究した。

Current Status of Research Progress
Current Status of Research Progress

3: Progress in research has been slightly delayed.

Reason

2020年初に始まったコロナ禍で、2019年度末に予定していた研究打合せと成果発表のための海外渡航や外国人共同研究者の招へいができなくなり、研究費の繰越が不可避となった。また、それ以後2年以上にわたり現在も続くコロナ感染拡大の影響で、特に2020年度は研究計画の大幅な練り直しを余儀なくされ、その影響は今に及んでいる。
そのような困難下でも、海外研究者との研究連絡や国際研究集会での成果発表はオンラインでの実施が普及しており、また研究の遅れを取り戻すために特定研究員などの雇用を行なっている。その結果、当初の研究計画は2年の遅れを経て概ね実施できたと考えている。

Strategy for Future Research Activity

コロナ禍の今後の状況はまだ予断を許さないが、それぞれの課題について、研究分担者とも緊密に協力しつつ、研究計画に沿って着実に研究を進める。

Report

(2 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report

Research Products

(55 results)

All 2021 2020 2019 2018 Other

All Int'l Joint Research (2 results) Journal Article (14 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 14 results,  Open Access: 6 results) Presentation (38 results) (of which Int'l Joint Research: 17 results,  Invited: 23 results) Funded Workshop (1 results)

  • [Int'l Joint Research] Rutgers University/Montana State University(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Imperial College London(英国)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Equilibria and their Stability in Networks with Steep Sigmoidal Nonlinearities2021

    • Author(s)
      Duncan William、Gedeon Tomas、Kokubu Hiroshi、Mischaikow Konstantin、Oka Hiroe
    • Journal Title

      SIAM J. Applied Dynamical Systems

      Volume: 20 Pages: 2108-2141

    • DOI

      10.1137/21m1398331

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Fractal mechanism of basin of attraction in passive dynamic walking2020

    • Author(s)
      Okamoto Kota、Aoi Shinya、Obayashi Ippei、Kokubu Hiroshi、Senda Kei、Tsuchiya Kazuo
    • Journal Title

      Bioinspiration & Biomimetics

      Volume: 15 Pages: 055002-055002

    • DOI

      10.1088/1748-3190/ab9283

    • NAID

      120006888011

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Visualization of the Dynamics Effect: Projection of on-the-Fly Trajectories to the Subspace Spanned by the Static Reaction Path Network2020

    • Author(s)
      Tsutsumi Takuro, Ono Yuriko, Arai Zin, Taketsugu Tetsuya
    • Journal Title

      Journal of Chemical Theory and Computation

      Volume: 16 Pages: 4029-4037

    • DOI

      10.1021/acs.jctc.0c00018

    • NAID

      120007044513

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hereditarily non uniformly perfect non-autonomous Julia sets2020

    • Author(s)
      Comerford Mark、Stankewitz Rich、Sumi Hiroki
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: 40 Pages: 33-33

    • DOI

      10.3934/dcds.2020002

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The Hausdorff dimension function of the family of conformal iterated function systems of generalized complex continued fractions2020

    • Author(s)
      Inui Kanji、Okada Hikaru、Sumi Hiroki
    • Journal Title

      Discrete and Continuous Dynamical Systems - A

      Volume: 40 Pages: 753-766

    • DOI

      10.3934/dcds.2020060

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hausdorff measures and packing measures of limit sets of CIFSs of generalized complex continued fractions2020

    • Author(s)
      Inui Kanji、Sumi Hiroki
    • Journal Title

      Journal of Difference Equations and Applications

      Volume: 26 Pages: 104-121

    • DOI

      10.1080/10236198.2019.1709063

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Explicit transversality conditions and local bifurcation diagrams for Bogdanov-Takens bifurcation on center manifolds2019

    • Author(s)
      Yang Li, Hiroshi Kokubu, and Kazuyuki Aihara
    • Journal Title

      Physica D: Nonlinear Phenomena

      Volume: 391 Pages: 52-65

    • DOI

      10.1016/j.physd.2018.11.005

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] The onset of transient turbulence in minimal plane Couette ow2019

    • Author(s)
      Julius Rhoan Lustro, Genta Kawahara, Lennaert van Veen, Masaki Shimizu, Hiroshi Kokubu
    • Journal Title

      J. Fluid Mech. Rapids

      Volume: 862 Pages: 1-15

    • DOI

      10.1017/jfm.2018.971

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Topological computation analysis of meteorological time-series data.2019

    • Author(s)
      Morita, H., M. Inatsu, and H. Kokubu
    • Journal Title

      SIAM Journal on Applied Dynamical Systems

      Volume: 18 Pages: 1200-1212

    • DOI

      10.1137/18m1184746

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Non-i.i.d. random holomorphic dynamical systems and the probability of tending to infinity2019

    • Author(s)
      Sumi Hiroki、Watanabe Takayuki
    • Journal Title

      Nonlinearity

      Volume: 32 Pages: 3742-3771

    • DOI

      10.1088/1361-6544/ab231e

    • Related Report
      2019 Annual Research Report 2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Hereditarily non-uniformly perfect sets2019

    • Author(s)
      R. Stankewitz, T. Sugawa and H. Sumi
    • Journal Title

      Discrete Contin. Dyn. Syst. Ser. S

      Volume: 12 Pages: 2391-2402

    • DOI

      10.3934/dcdss.2019150

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On Parameter Loci of the Henon Family2018

    • Author(s)
      Arai Zin、Ishii Yutaka
    • Journal Title

      Communications in Mathematical Physics

      Volume: 361 Pages: 343-414

    • DOI

      10.1007/s00220-018-3174-0

    • NAID

      120006940730

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Boundary of the horseshoe locus for the Henon family2018

    • Author(s)
      Z. Arai, Y. Ishii, H. Takahasi
    • Journal Title

      SIAM Journal on Applied Dynamical Systems

      Volume: 17 Pages: 2234-2248

    • DOI

      10.1137/18m1174684

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A visualization of the intrinsic reaction coordinate and global reaction route map by classical multidimensional scaling2018

    • Author(s)
      Takuro Tsutsumi, Yuriko Ono, Zin Arai, Tetsuya Taketsugu
    • Journal Title

      J. Chem. Theory Comput.

      Volume: 14 Pages: 4263-4270

    • DOI

      10.1021/acs.jctc.8b00176

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Presentation] Learning dynamics of the logistic maps by Reservoir Computing2021

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      International Conference: Differential Equations for Data Science 2021
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 力学系のリザバー計算2021

    • Author(s)
      國府寛司
    • Organizer
      東京理科大学 第2回数理・AIセミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] 力学系のリザバー計算:ロジスティック写像の場合2021

    • Author(s)
      國府寛司
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] 力学系のリザバー計算:ある数学的枠組み2021

    • Author(s)
      國府寛司
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Period doubling bifurcations from complex and algebraic point of view2020

    • Author(s)
      Z. Arai
    • Organizer
      Rutgers University Dynamical System Seminar
    • Related Report
      2019 Annual Research Report
  • [Presentation] Non-uniformly perfect Julia sets of non-autonomous dynamics of unbounded sequences of polynomials2020

    • Author(s)
      角大輝
    • Organizer
      2019年度冬の力学系研究集会(2020年1月10日-13日)、日本大学軽井沢研修所
    • Related Report
      2018 Annual Research Report
  • [Presentation] Period doubling bifurcations from complex and algebraic points of view2020

    • Author(s)
      Zin Arai
    • Organizer
      Dynamical Systems Seminar, Rutgers University, USA
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Morse decomposition of dynamics from time-series data2019

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Workshop on Data Analysis and Machine Learning in Dynamical Systems
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      Hiroki Sumi
    • Organizer
      Thermodynamic Formalism – Applications to Geometry, Number Theory, and Stochastics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      Hiroki Sumi
    • Organizer
      The 2019 Fall Program of Low-Dimensional Dynamics, Shanghai Center for Mathematical Sciences
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      角大輝
    • Organizer
      数理解析研究所研究集会「ランダム力学系理論とフラクタル幾何学の研究」
    • Related Report
      2019 Annual Research Report
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      角大輝
    • Organizer
      第9回岐阜数理科学研究会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      角大輝
    • Organizer
      研究集会「エルゴード理論とその周辺」
    • Related Report
      2019 Annual Research Report
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      角大輝
    • Organizer
      数理解析研究所研究集会「複素力学系の分岐と安定性の研究」
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] On the gradient structure of chemical reactions2019

    • Author(s)
      荒井迅
    • Organizer
      RIMS 研究集会: 力学系–新たな理論と応用に向けて–
    • Related Report
      2019 Annual Research Report
  • [Presentation] On period doubling bifurcations2019

    • Author(s)
      荒井迅
    • Organizer
      第 9 回岐阜数理科学研究会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      Hiroki Sumi
    • Organizer
      Workshop on Random Dynamical Systems and Anomalous Dynamics, Imperial College London, ロンドン、イギリス
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      角大輝
    • Organizer
      2018年度冬の力学系研究集会、 日本大学軽井沢研修所
    • Related Report
      2018 Annual Research Report
  • [Presentation] On the monodromy and period doubling bifurcations of the He'non map2019

    • Author(s)
      Zin Arai
    • Organizer
      Real and Complex Dynamics of He'non's Map, 慶應大学, 2019年3月
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Morse decomposition of dynamics from time-series data,2019

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Workshop on Data Analysis and Machine Learning in Dynamical Systems, Faculty of Sciences, University of Tokyo
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Morse decomposition of dynamics from time-series data and its application2019

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      EASIAM Wuhan University, Wuhan, China June 13-16, 2019
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      Hiroki Sumi
    • Organizer
      Thermodynamic Formalism; Applications to Geometry, Number Theory, and Stochastics (2019年7月8日ー12日), Institut Mittag-Leffler, スウェーデン
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      Hiroki Sumi
    • Organizer
      The 2019 Fall Program of Low-Dimensional Dynamics, Shanghai Center for Mathematical Sciences (2019年9月23日ー27日), Fudan University, 上海、中国
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      Hiroki Sumi
    • Organizer
      数理解析研究所研究集会「Research on the Theory of Random Dynamical Systems and Fractal Geometry」(2019年8月29日ー9月2日)、京都大学
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      角大輝
    • Organizer
      第9回岐阜数理科学研究会(2020年9月9日--11日)、飛騨高山まちの博物館研修室、岐阜県高山市
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2019

    • Author(s)
      角大輝
    • Organizer
      研究集会「エルゴード理論とその周辺」(2020年11月20日ー23日)、 新潟県長岡市まちなかキャンパス
    • Related Report
      2018 Annual Research Report
  • [Presentation] Random holomorphic dynamical systems associated with analytic families of holomorphic maps2019

    • Author(s)
      角大輝
    • Organizer
      数理解析研究所研究集会「複素力学系の分岐と安定性の研究」(2020年12月9日--13日)、数理解析研究所
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the gradient structure of chemical reactions2019

    • Author(s)
      荒井迅
    • Organizer
      力学系―新たな理論と応用に向けて―, 数理解析研究所
    • Related Report
      2018 Annual Research Report
  • [Presentation] On period doubling bifurcations2019

    • Author(s)
      荒井迅
    • Organizer
      第9回岐阜数理科学研究会, 飛騨高山まちの博物館
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 計算トポロジーと位相的データ解析2019

    • Author(s)
      荒井迅
    • Organizer
      東京工業大学情報理工学院寺子屋セミナー, 東京工業大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Computer-assisted Approach to Global Dynamics of Multi-parameter Systems2018

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      KSIAM Spring Conference KAIST, Daejeon, South Korea
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Morse decomposition of the switching system and its smooth perturbations2018

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      International Conference on Algebraic Topology in Data and Dyamics, Montana State University, Bozeman, USA
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2018

    • Author(s)
      Hiroki Sumi
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 台北
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2018

    • Author(s)
      角大輝
    • Organizer
      研究集会「エルゴード理論とその周辺」、大阪大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Classification of generic random holomorphic dynamical systems associated with analytic families of rational maps2018

    • Author(s)
      角大輝
    • Organizer
      複素力学系研究とその発展 、京都大学数理解析研究所
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The Conley index for the real and complex He'non maps2018

    • Author(s)
      Zin Arai
    • Organizer
      International Conference on Algebraic Topology in Data and Dyamics, Montana State University, Bozeman, USA
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 力学系の大域的な分岐とその計算について2018

    • Author(s)
      荒井迅
    • Organizer
      岩手数理科学セミナー, 岩手大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 化学反応経路網の幾何学的理解に向けて2018

    • Author(s)
      荒井迅
    • Organizer
      日本応用数理学会2018年度年会, 名古屋大学
    • Related Report
      2018 Annual Research Report
  • [Funded Workshop] 数理解析研究所研究集会「Research on the Theory of Random Dynamical Systems and Fractal Geometry」2019

    • Related Report
      2018 Annual Research Report

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Published: 2018-04-23   Modified: 2022-12-28  

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