Stochastic chaos in random dynamical systems
| Project/Area Number |
18K03441
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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| Research Institution | Hokkaido University |
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Principal Investigator |
Sato Yuzuru 北海道大学, 電子科学研究所, 准教授 (30342794)
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| Co-Investigator(Kenkyū-buntansha) |
角 大輝 京都大学, 人間・環境学研究科, 教授 (40313324)
矢野 孝次 京都大学, 理学研究科, 准教授 (80467646)
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | ランダム力学系 / 確率分岐 / 確率カオス / 計算機援用証明 / random dynamical systems / stochastic bifurcation / random strange attractor / stochastic chaos / comput. ergodic theory / 不確定性 / 大自由度力学系 |
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| Outline of Final Research Achievements |
Based on experimental time series analysis and modeling for large scale nonlinear phenomena, we quantitatively studied physical properties of stochastic chaos and contribute to studies on nonlinear stochastic phenomena systematically. Integrating former studies on noise-induced phenomena, we produce a phenomenology on noise-induced phenomena and apply it to real physical systems. The achieved results is as follows. (1) Expanding knowledge on noise-induced phenomena and stochastic bifurcation and give a computer-assisted proof on multiple noise-induced transitions. (2) We found stochastic chaos in fluid flow turbulence and climate dynamics through experimental time series analysis and modeling. (3) Random dynamical system approaches to machine learning and other algorithms and their concrete applications are shown.
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| Academic Significance and Societal Importance of the Research Achievements |
ランダム・ストレンジ・アトラクターによって生成される確率カオスという普遍的な現象が，乱流や気象現象のみならず，その他の大規模な非線形現象にも見出されていく可能性が高まった。様々な大規模な非線形現象のランダム力学系理論に基づく分析や，実験時系列からの高精度のモデル抽出法，その予測制御の解析により，非線形複雑系の数理科学が深化されてい
くことが見込まれる。さらに, ここで提案された研究手法は, これまで困難だった気象の長期予測への貢献のみならず，経済変動や環境変動の予測など，社会，経済，環境の問題を解明する新たな解析法となることが期待される。
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Report
(5 results)
Research Products
(102 results)
