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The development of the topological and computational methods on dynamical systems

Research Project

Project/Area Number 24540222
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionRyukoku University

Principal Investigator

Oka Hiroe  龍谷大学, 理工学部, 教授 (20215221)

Co-Investigator(Renkei-kenkyūsha) KOKUBU Hiroshi  京都大学, 大学院理学研究科, 教授 (50202057)
ARAI Jin  北海道大学, 理学系研究科, 准教授 (80362432)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords力学系 / モース分解 / 大域的構造 / 時系列 / 全構造計算 / 制御ネットワーク系 / データ解析 / パーシステンス・ホモロジー / 乱流データ / global attractor / dynamical systems / time series / topological / computational / morse decomposition / topology / data analysis / unstable invariant set / rigorous computation / regulatory network / 不変集合 / 分岐 / トポロジー / 厳密計算
Outline of Final Research Achievements

Topological-computational method (database schema) is our original approach in order to overcome the weak point of the analysis of real dynamical systems. The theory and an application (2-dim’l discrete dynamical system called Leslie model) is discussed in our paper. Also, boundary crisis, which is typical in the global bifurcations is studied in this methods, and obtain a theorem using a notion of chain orbit.
A switching network is a simple model for gene regulatory network representing the regulation of proteins, and we study the database of such systems. Moreover we treat the time series data of some gene regulatory network, from which we obtain a Morse decomposition, which is same as the one from a different method. We also study the graphical time series obtained by 3-D turbulence and get some computational results wrt persistence homology.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (17 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (11 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results) Remarks (4 results)

  • [Journal Article] A topological computation approach to the interior crisis bifurcation2013

    • Author(s)
      Hiroshi Kokubu and Hiroe Oka
    • Journal Title

      Nonlinear Theory and Its Applications, IEICE

      Volume: 4 Issue: 1 Pages: 97-103

    • DOI

      10.1587/nolta.4.97

    • NAID

      130003375415

    • ISSN
      2185-4106
    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Graph-based topological approximation of saddle-node bifurcation in maps2012

    • Author(s)
      Z. Arai, M. Gameiro, T. Gedeon, H. Kokubu, H.Oka & K. Mischaikow
    • Journal Title

      RIMS Kokyuroku Bessatsu B

      Volume: 31 Pages: 225-241

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 遺伝子ネットワークの時系列を用いたモース分解2016

    • Author(s)
      岡宏枝
    • Organizer
      武蔵野大学・明治大学・龍谷大学合同シンポジウム
    • Place of Presentation
      龍谷大学瀬田学舎1号館534号室
    • Year and Date
      2016-02-10
    • Related Report
      2015 Annual Research Report
  • [Presentation] Morse decomposition of regulatory networks via determining nodes2015

    • Author(s)
      Hiroe Oka
    • Organizer
      Fall Eastern Sectional Meeting,AMS,Meeting
    • Place of Presentation
      Rutgers University, New Brunswick, NJ
    • Year and Date
      2015-11-14
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 遺伝子ネットワーク時系列データによるグローバル・アトラクタのモース分解について2015

    • Author(s)
      岡宏枝(国府宏枝)
    • Organizer
      冬の力学系研究集会
    • Place of Presentation
      日本大学 軽井沢研修所
    • Year and Date
      2015-01-09 – 2015-01-12
    • Related Report
      2014 Research-status Report
  • [Presentation] Detecting Morse decompositions of the global attractor of regulatory networks by time series data2014

    • Author(s)
      岡宏枝(国府宏枝)
    • Organizer
      Computational Dynamics", Foundations of Computational Mathematics,
    • Place of Presentation
      Montevideo, Urguay,
    • Year and Date
      2014-12-11 – 2014-12-20
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 遺伝子ネットワークの時系列解析2014

    • Author(s)
      岡 宏枝
    • 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302講義室
    • Related Report
      2013 Research-status Report
  • [Presentation] Detecting Morse Decompositions of the Global Attractor of Regulatory Networks by Time Series Data2014

    • Author(s)
      Hiroe Oka
    • Organizer
      Algebraic Topology in Dynamics, Differential Equations, and Experimental Data
    • Place of Presentation
      Univ. of Minnesota, IMA,(アメリカ合衆国)
    • Related Report
      2013 Research-status Report
  • [Presentation] Detecting Morse decompositions of the global attractor of regulatory networks by time series data2014

    • Author(s)
      岡 宏枝
    • Organizer
      RIMS研究集会 力学系理論の諸分野への応用の新展開
    • Place of Presentation
      RIMS,(京都大学)
    • Related Report
      2013 Research-status Report
  • [Presentation] A Monodromy Example2013

    • Author(s)
      Hiroe Oka
    • Organizer
      V Developers Workshop on the Conley-Morse Database Project
    • Place of Presentation
      Kyoto, Japan
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Bifurcations of Conley-Morse graphs: Crisis and Monodromy2013

    • Author(s)
      Hiroe Oka
    • Organizer
      Conference on Dynamics of Differential Equations
    • Place of Presentation
      Atlanta, USA
    • Related Report
      2012 Research-status Report
  • [Presentation] A topological-computation approach to the crisis bifurcations2012

    • Author(s)
      Hiroe Oka
    • Organizer
      DYNAMICS, TOPOLOGY AND COMPUTATIONS
    • Place of Presentation
      BĘDLEWO, POLAND
    • Related Report
      2012 Research-status Report
  • [Presentation] Topological crisis bifurcation2012

    • Author(s)
      Hiroe Oka
    • Organizer
      International Conference ”Dynamical Systems:100 years after Poincare
    • Place of Presentation
      Gijon, Spain
    • Related Report
      2012 Research-status Report
  • [Remarks] AMS Sectional Meeting Program

    • URL

      http://www.ams.org/meetings/sectional/2227_program.html

    • Related Report
      2015 Annual Research Report
  • [Remarks] Hiore Okaのホームページ

    • URL

      http://www.math.ryukoku.ac.jp/~oka/

    • Related Report
      2014 Research-status Report
  • [Remarks] Hiroe"s home page

    • URL

      http://www.math.ryukoku.ac.jp/~oka/

    • Related Report
      2013 Research-status Report
  • [Remarks] Hiroe's Home Page!

    • URL

      http://www.math.ryukoku.ac.jp/~oka/

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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