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Development and Application of Topological Computation Theory for Dynamical Systems

Research Project

Project/Area Number 25287029
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionKyoto University

Principal Investigator

Kokubu Hiroshi  京都大学, 理学研究科, 教授 (50202057)

Co-Investigator(Renkei-kenkyūsha) HIRAOKA Yasuaki  東北大学, 材料科学高等研究所, 教授 (10432709)
ARAI Zin  中部大学, 創発学術院, 教授 (80362432)
TAKAHASHI Hiroki  慶応義塾大学, 理工学部, 准教授 (00467440)
SAKAJO Takashi  京都大学, 大学院理学研究科, 教授 (10303603)
MOCHIZUKI Atsushi  理化学研究所, 望月理論生物学研究室, 主任研究員 (10304726)
INATSU Masaru  北海道大学, 理学研究院, 教授 (80422450)
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥18,200,000 (Direct Cost: ¥14,000,000、Indirect Cost: ¥4,200,000)
Fiscal Year 2016: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥7,150,000 (Direct Cost: ¥5,500,000、Indirect Cost: ¥1,650,000)
Keywords力学系 / トポロジー / 計算機援用解析 / 時系列 / 気象学 / 位相計算 / 生命科学 / ネットワーク
Outline of Final Research Achievements

Combining ideas and methods from Topology and Coputation, a new method, called the topological computation theory for global structures of dynamical systems, has been developed in order to give better understandings of dynamics appearing in various fields of Science and Technology. As its applications, studied are network dynamics such as the gene regulatory network in the Life Science, as well as the development of a new dynamical time-series analysis method which extracts information on underlying dynamics from noisy time-series data such as meteorological observation data.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • 2015 Annual Research Report
  • 2014 Annual Research Report
  • 2013 Annual Research Report
  • Research Products

    (32 results)

All 2018 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (8 results) Journal Article (5 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 5 results,  Acknowledgement Compliant: 1 results) Presentation (18 results) (of which Int'l Joint Research: 9 results,  Invited: 13 results) Funded Workshop (1 results)

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

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Rutgers University/Montana State University(米国)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Free University of Berlin(Germany)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] University of Sao Paulo, Sao Carlos(Brazil)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Rutgers University/Montana State University(米国)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Free University of Berlin(Germany)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Institute of Science and Technology(Austria)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] University of Sao Paulo Sao Carlos(Brazil)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Global dynamics for steep nonlinearities in two dimensions2017

    • Author(s)
      Tomas Gedeon, Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Hiroe Oka
    • Journal Title

      Physica D

      Volume: 339 Pages: 18-38

    • DOI

      10.1016/j.physd.2016.08.006

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] A study of rigorous ODE integrators for multi-scale set-oriented computations2016

    • Author(s)
      Tomoyuki Miyaji, Pawel Pilarczyk, Marcio Gameiro, Hiroshi Kokubu, and Konstantin Mischaikow
    • Journal Title

      Applied Numerical Mathematics

      Volume: 107 Pages: 34-47

    • DOI

      10.1016/j.apnum.2016.04.005

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Inducing a map on homology from a correspondence2016

    • Author(s)
      Shaun Harker, Hiroshi Kokubu, Konstantin Mischaikow, Pawel Pilarczyk
    • Journal Title

      Proceedings of American Mathematical Society

      Volume: 144 Issue: 4 Pages: 1787-1801

    • DOI

      10.1090/proc/12812

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Inducing a Map on Homology from a Correspondence2015

    • Author(s)
      S. Harker, H. Kokubu, K. Mischaikow, P. Pilarczyk
    • Journal Title

      Proceedings of American Mathematical Society

      Volume: 未定

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] About the unfolding of the Hopf-zero singularity2013

    • Author(s)
      Freddy Dumortier, Santiago Ibanez, Hiroshi Kokubu, and Carles Simo
    • Journal Title

      Discrete and Continuous Dynamical Systems A

      Volume: 33 Issue: 10 Pages: 4435-4471

    • DOI

      10.3934/dcds.2013.33.4435

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Presentation] Stability and bifurcations of some simple models of the human bipedal locomotion2018

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      The Third International Conference on the Dynamics of Differential Equations
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Stability of bipedal locomotion: a dynamical system approach2017

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      2017 International Workshop on Industrial and Applied Mathematics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Global dynamics of systems with steep nonlinearities2017

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Mathematical Congress of the Americas
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Computer-assisted methods for detecting global structure of dynamics2016

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      SCAN 2016
    • Place of Presentation
      Uppsala University, Uppsala, Sweden
    • Year and Date
      2016-09-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Morse Decompositions of Regulatory Networks via determining nodes2016

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      International Conference "Patterns and Waves 2016
    • Place of Presentation
      Hokkaido Universiy, Sapporo, Japan
    • Year and Date
      2016-08-01
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological Computation Theory for Global Dynamics of Multi-Parameter Systems2016

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      International Conference on Difference Equations and Applications 2016
    • Place of Presentation
      I-site Namba, Osaka Prefectural University, Osaka, Japan
    • Year and Date
      2016-07-25
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Dynamical time-series analysis for Morse decomposition - an application to meteorological data with noise -2015

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Workshop on Stochastic Dynamics
    • Place of Presentation
      Chinese Academy of Science, Beijing, China
    • Year and Date
      2015-08-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Morse decomposition of regulatory networks via its determining nodes2015

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Mini-symposium "Dynamics of Chemical, Metabolic, and Gene Regulatory Networks", Equadiff 2015
    • Place of Presentation
      Lyon, France
    • Year and Date
      2015-07-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Morse decompositions of dynamical systems from time-series data2015

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      2015 NCTS Workshop on Dynamical Systems
    • Place of Presentation
      National Center for Theoretical Sciences, National Taiwan University, Taipei, Taiwan
    • Year and Date
      2015-05-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 力学系の位相計算的時系列解析法とその気象学への応用の試み2014

    • Author(s)
      國府寛司
    • Organizer
      研究集会「非線形現象の数理」
    • Place of Presentation
      休暇村紀州加太, 和歌山市
    • Year and Date
      2014-12-26 – 2014-12-28
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data2014

    • Author(s)
      國府寛司
    • Organizer
      第5回「ハミルトン系とその周辺」研究集会
    • Place of Presentation
      金沢大学サテライトプラザ
    • Year and Date
      2014-05-29 – 2014-05-31
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data2014

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      2014 ICIAM Scientific Workshop
    • Place of Presentation
      Mathematical Bioscience Institute, Ohio State Univerity Columbus, U.S.A.
    • Year and Date
      2014-05-15 – 2014-05-16
    • Related Report
      2014 Annual Research Report
  • [Presentation] Analysis of Global Dynamics from Time-series Data: Case Studies2014

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      IMA Workshop “Algebraic Topology in Dynamics, Differential Equations, and Experimental Data”
    • Place of Presentation
      IMA, U Minnesota, USA
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A topological computation method for global dynamics and its applications2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      Workshop on Industrial and Applied Mathematics
    • Place of Presentation
      Chinese Academy of Science, Beijing, P.R. China
    • Related Report
      2013 Annual Research Report
  • [Presentation] ダイナミクス全構造計算による力学系の相空間構造解析の方法とその応用2013

    • Author(s)
      國府寛司
    • Organizer
      第1回ダイナミクス研究会中野
    • Place of Presentation
      明治大学中野キャンパス
    • Related Report
      2013 Annual Research Report
  • [Presentation] Dynamical time series analysis using a topological computation method2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      2013 Northeastern Asian Symposium on High Performance Computing Methods and Modeling
    • Place of Presentation
      Chengdu, China
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] 遺伝子ネットワークの力学系理論2013

    • Author(s)
      國府寛司
    • Organizer
      RIMS共同研究「力学系・トポロジーの生命科学・物質科学への応用」
    • Place of Presentation
      アクティプラザ琵琶,滋賀県
    • Related Report
      2013 Annual Research Report
  • [Presentation] Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data2013

    • Author(s)
      Hiroshi Kokubu
    • Organizer
      IMA Workshop “Topological Structures in Computational Biology”
    • Place of Presentation
      IMA, U Minnesota, USA
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Funded Workshop] Kyoto Dynamics Days: Random Dynamical Systems Theory and Its Applications2017

    • Related Report
      2017 Annual Research Report

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Published: 2013-05-21   Modified: 2022-02-21  

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