Control of solutions to multi-component reaction diffusion system

• Project/Area Number: 26400214
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Meiji 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, 専任准教授 (80542274)
• Co-Investigator(Renkei-kenkyūsha): SAKAMOTO Takashi 明治大学, 理工学部, 講師 (30546891)
• Research Collaborator: OHNO Kota
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
• Keywords: 反応拡散系 / 大域フィードバック / Turing不安定化 / 自己組織化 / パターンの制御 / 光制御BZ反応 / 倍周期分岐 / 結合振動子 / 定在波 / 交互振動 / 反位相解 / パターン制御

Outline of Final Research Achievements

The purpose of this project is to develop the method of stabilization of the desired patterns by feedback control both theoretically and experimentally. Since activator-inhibitor system which has control input to the activator is semi-passive we can stabilize both stationary and oscillatory patterns. It turns out that we can construct an experimental feedback control system by using photo sensitive BZ reaction although it is not semi-passive. We have checked this fact by simulation for the mathematical model and real experiment.

Research Products

• [Journal Article] Rippling rectangular waves for a modified Benney equation (2018)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Evolution of Self-Propelled Objects: From the Viewpoint of Nonlinear Science (2018)
  • 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
  • Peer Reviewed / Open Access
• [Journal Article] Asymmetries in leaf branch are associated with differential speeds along growth axes: A theoretical prediction (2017)
  • 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
  • Peer Reviewed
• [Journal Article] Stability of periodic traveling waves in the Aliev-Panfilov reaction-diffusion system (2016)
  • Author(s): M. Osman Gani and Toshiyuki Ogawa
  • Journal Title: Communications in Nonlinear Science and Numerical Simulation Volume: 33 Pages: 30-42
  • DOI: 10.1016/j.cnsns.2015.09.002
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Chaotic Dynamics in an Integro-Differential Reaction-Diffusion System in the Presence of 0:1:2 Resonance (2016)
  • Author(s): T.Ogawa and T.O.Sakamoto
  • Journal Title: in “Mathematical Fluid Dynamics, Present and Future”, Springer Proceedings in Mathematics & Statistics Volume: 183 Pages: 531-562
  • Peer Reviewed
• [Journal Article] Oscillation of speed of a self-propelled Belousov-Zhabotinsky droplet (2016)
  • Author(s): N. J. Suematsu, Y. Mori, T. Amemiya, S. Nakata
  • Journal Title: The Journal of Physical Chemistry Letters Volume: 7 Issue: 17 Pages: 3424-3428
  • DOI: 10.1021/acs.jpclett.6b01539
  • Peer Reviewed
• [Journal Article] Selective pattern formation control: Spatial spectrum consensus and Turing instability approach (2015)
  • Author(s): K.Kashima, T.Ogawa and T.Sakurai
  • Journal Title: Automatica Volume: 56 Pages: 25-35
  • DOI: 10.1016/j.automatica.2015.03.019
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Selective Stabilization of Unstable Standing Waves in a Reaction-diffusion System (2015)
  • Author(s): 梅津 佑介, 小川 知之, 加嶋 健司
  • Journal Title: Transactions of the Society of Instrument and Control Engineers Volume: 51 Issue: 2 Pages: 110-119
  • DOI: 10.9746/sicetr.51.110
  • NAID: 130004855734
  • ISSN: 0453-4654, 1883-8189
  • Peer Reviewed
• [Journal Article] Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers (2014)
  • Author(s): T. Fatima, E.R. IJioma, T. Ogawa and A. Muntean
  • Journal Title: Networks and Heterogeneous Media Volume: 9(4) Issue: 4 Pages: 709-737
  • DOI: 10.3934/nhm.2014.9.709
  • Peer Reviewed
• [Journal Article] Alternans and spiral breakup in an excitable reaction-diffusion system: a simulation study (2014)
  • Author(s): M Osman Gani and Toshiyuki Ogawa
  • Journal Title: International Scholarly Research Notices Volume: 2014 Pages: 459675-459675
  • DOI: 10.1155/2014/459675
  • Peer Reviewed / Open Access
• [Presentation] さざ波立つ矩形波へのトーラス分岐 (2017)
  • Author(s): 宮路智行、小川知之、関坂歩幹
  • Organizer: 日本数学会2017年年会
  • Place of Presentation: 首都大学東京南大沢キャンパス
  • Year and Date: 2017-03-27
• [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
• [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
• [Presentation] 振動場Oregonator modelの大域的制御 (2016)
  • Author(s): 大野航太, 小川知之, 末松信彦
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Year and Date: 2016-12-16
• [Presentation] Drift bifurcation of traveling wave in reaction-diffusion system with 3 competing species (2016)
  • Author(s): T.Ogawa
  • Organizer: Joint Australia-Japan workshop on dynamical systems with applications in life sciences
  • Place of Presentation: Queensland University of Technology, Brisbane, Australia
  • Year and Date: 2016-07-18
  • Int'l Joint Research
• [Presentation] ３種反応拡散系の進行波解のドリフト分岐 (2015)
  • Author(s): 小川知之
  • Organizer: 研究集会「多変数反応拡散系の数理とその周辺」
  • Place of Presentation: 神戸大学深江キャンパス
  • Year and Date: 2015-12-25
• [Presentation] Stabilization of Unstable Standing Waves in Reaction-diffusion Systems (2014)
  • Author(s): Toshiyuki OGAWA
  • Organizer: The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Madrid, Spain
  • Year and Date: 2014-07-08