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Controlling multi-stable oscillatory system using mathematical structure

Research Project

Project/Area Number 17K05375
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionMeiji University

Principal Investigator

Ogawa Toshiyuki  明治大学, 総合数理学部, 専任教授 (80211811)

Co-Investigator(Kenkyū-buntansha) 末松 信彦  明治大学, 総合数理学部, 専任教授 (80542274)
Project Period (FY) 2017-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords反応拡散系 / BZ化学反応 / パターンの制御 / 大域フィードバック / リコネクション / 進行波解 / 振動場反応拡散系 / オレゴネーターモデル / 振動場 / BZ反応 / 大域フィードバック制御 / 光制御BZ反応系 / 大域抑制結合 / 同期振動 / 反位相同期 / 交互振動 / パターンダイナミクス / 振動パターン / 大域制御
Outline of Final Research Achievements

This study aims to clarify the solution structure and dynamics of oscillatory reaction-diffusion systems and to integrate experimental and theoretical studies. A light-sensitive feedback system using the BZ chemical reaction is considered, and corresponding experimental systems are constructed. Bifurcation analysis of the diffusion coupling of oscillators was performed using the corresponding optically controlled Oregonator model, and period-doubling bifurcation and reconnection phenomena were confirmed. We showed the possibility of controlling the state of the system by the competition between diffusion and feedback, and showed that the corresponding control is actually possible in the experimental system. Furthermore, we analyzed the stability of the vibration patterns appearing in the seminiferous tubules. These are paving the way for the study of pattern dynamics on metric graphs and chimera oscillations appearing in large-scale coupled oscillator systems.

Academic Significance and Societal Importance of the Research Achievements

本研究の学術的意義は、振動場反応拡散系の解構造とダイナミクスを解明し、理論と実験を融合させることである。大域フォードバックを利用した解析手法の提案や系の豊富な解構造が明らかになり、振動パターンの制御に向けた新たな手法の展開に寄与した。そのほか、生理学や生態学に現れる様々な振動パターンの解明を行っており、本研究課題で得られた手法は、複雑な系の理解に貢献しうるものと言える。

Report

(7 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (21 results)

All 2023 2022 2021 2020 2019 2018 2017

All Journal Article (10 results) (of which Int'l Joint Research: 4 results,  Peer Reviewed: 10 results,  Open Access: 4 results) Presentation (10 results) (of which Int'l Joint Research: 1 results) Book (1 results)

  • [Journal Article] Bifurcation of co-existing traveling wave solutions in a three-component competition--diffusion system2023

    • Author(s)
      Shin-Ichiro Ei, Hideo Ikeda, Toshiyuki Ogawa
    • Journal Title

      Physica D

      Volume: 448 Pages: 133703-133703

    • DOI

      10.1016/j.physd.2023.133703

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Inhibitor-Induced Wavetrains and Spiral Waves in an Extended FitzHugh?Nagumo Model of Nerve Cell Dynamics2022

    • Author(s)
      Gani M. Osman、Kabir M. Humayun、Ogawa Toshiyuki
    • Journal Title

      Bulletin of Mathematical Biology

      Volume: 84 Issue: 12 Pages: 145-145

    • DOI

      10.1007/s11538-022-01100-9

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Mathematical Modeling of Dynamic Cellular Association Patterns in Seminiferous Tubules2021

    • Author(s)
      Kawamura Mari、Sugihara Kei、Takigawa-Imamura Hisako、Ogawa Toshiyuki、Miura Takashi
    • Journal Title

      Bulletin of Mathematical Biology

      Volume: 83 Issue: 4 Pages: 33-33

    • DOI

      10.1007/s11538-021-00863-x

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence and stability of non-monotone travelling wave solutions for the diffusive Lotka?Volterra system of three competing species2020

    • Author(s)
      Chang Chueh-Hsin、Chen Chiun-Chuan、Hung Li-Chang、Mimura Masayasu、Ogawa Toshiyuki
    • Journal Title

      Nonlinearity

      Volume: 33 Issue: 10 Pages: 5080-5110

    • DOI

      10.1088/1361-6544/ab9244

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Chemical Wave Propagation in the Belousov?Zhabotinsky Reaction Controlled by Electrical Potential2019

    • Author(s)
      Kuze Masakazu、Horisaka Mari、Suematsu Nobuhiko J.、Amemiya Takashi、Steinbock Oliver、Nakata Satoshi
    • Journal Title

      The Journal of Physical Chemistry A

      Volume: 123 Issue: 23 Pages: 4853-4857

    • DOI

      10.1021/acs.jpca.9b02636

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Competition between global feedback and diffusion in coupled Belousov-Zhabotinsky oscillators2019

    • Author(s)
      Ohno Kota、Ogawa Toshiyuki、Suematsu Nobuhiko J.
    • Journal Title

      Physical Review E

      Volume: 99 Issue: 1 Pages: 12208-12208

    • DOI

      10.1103/physreve.99.012208

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Spiral breakup in a RD system of cardiac excitation due to front?back interaction2018

    • Author(s)
      Gani M. Osman、Ogawa Toshiyuki
    • Journal Title

      Wave Motion

      Volume: 79 Pages: 73-83

    • DOI

      10.1016/j.wavemoti.2018.02.010

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Rippling rectangular waves for a modified Benney equation2018

    • Author(s)
      Miyaji Tomoyuki、Ogawa Toshiyuki、Sekisaka Ayuki
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics

      Volume: 印刷中 Issue: 2 Pages: 939-968

    • DOI

      10.1007/s13160-018-0304-1

    • NAID

      210000166795

    • Related Report
      2018 Research-status Report 2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Evolution of Self-Propelled Objects: From the Viewpoint of Nonlinear Science2018

    • Author(s)
      Suematsu Nobuhiko J.、Nakata Satoshi
    • Journal Title

      Chemistry - A European Journal

      Volume: 24 Issue: 24 Pages: 6308-6324

    • DOI

      10.1002/chem.201705171

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymmetries in leaf branch are associated with differential speeds along growth axes: A theoretical prediction2017

    • Author(s)
      Akiko Nakamasu, Nobuhiko J. Suematsu, Seisuke Kimura
    • Journal Title

      Developmental Dynamics

      Volume: 246 Issue: 12 Pages: 981-991

    • DOI

      10.1002/dvdy.24587

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Presentation] Stability of traveling wave in nonlocally coupled oscillator system2023

    • Author(s)
      大野航太,小川知之
    • Organizer
      日本数学会年会
    • Related Report
      2022 Annual Research Report
  • [Presentation] 振動場反応拡散系に現れるセグメントパターンの安定性について2023

    • Author(s)
      関坂歩幹,小川知之
    • Organizer
      日本数学会年会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Compact metric graph上のTuring不安定性2023

    • Author(s)
      小川知之,小林俊介
    • Organizer
      日本数学会年会
    • Related Report
      2022 Annual Research Report
  • [Presentation] Four-scroll attractor modelの幾何学的構造について2021

    • Author(s)
      小川知之,関坂歩幹
    • Organizer
      2021日本数学会秋季総合分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] Oscillatory behaviors observed in nonlocally coupled FitzHugh-Nagumo system2021

    • Author(s)
      大野航太,小川知之
    • Organizer
      2021年度応用数学合同研究集会
    • Related Report
      2021 Research-status Report
  • [Presentation] Bifurcation of a non-trivial traveling wave solution in a 3-component competition-diffusion system2021

    • Author(s)
      小川知之,栄伸一郎,池田榮雄,三村昌泰
    • Organizer
      日本数学会2021年会
    • Related Report
      2020 Research-status Report
  • [Presentation] BZ 反応振動子系への大域的フィードバック制御2018

    • Author(s)
      大野航太、小川知之、末松信彦
    • Organizer
      応用数理学会2018年 年会
    • Related Report
      2018 Research-status Report
  • [Presentation] Rippling Rectangular Waves for a Modified Benney Equation2018

    • Author(s)
      Toshiyuki Ogawa
    • Organizer
      The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] BZ 反応を用いた反応拡散系の大域的制御2017

    • Author(s)
      大野航太、小川知之、末松信彦
    • Organizer
      2017 年度応用数 学合同研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] BZ 反応を用いた振動場反応拡散系の大域的制御2017

    • Author(s)
      大野航太、小川知之、末松信彦
    • Organizer
      第 27 回 非 線形反応と協同現象研究会
    • Related Report
      2017 Research-status Report
  • [Book] 数理モデルとシミュレーション2020

    • Author(s)
      小川 知之、宮路 智行
    • Total Pages
      208
    • Publisher
      サイエンス社
    • ISBN
      9784781914954
    • Related Report
      2020 Research-status Report

URL: 

Published: 2017-04-28   Modified: 2024-01-30  

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