Controlling multi-stable oscillatory system using mathematical structure

2022 Fiscal Year Final Research Report

• Project/Area Number: 17K05375
• 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, 専任教授 (80542274)
• Project Period (FY): 2017-04-01 – 2023-03-31
• 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

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.

Free Research Field

応用数学

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。