2019 Fiscal Year Final Research Report
Search for a Sign of Critical Transition based on the Theory of Dynamical Systems
| Project/Area Number |
26310208
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2014-07-18 – 2020-03-31
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| Keywords | 力学系 / 臨界的遷移 / 分岐 / 位相的方法 / 時系列 / 大域的構造 / ノイズ / モース分解 |
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| Outline of Final Research Achievements |
A large-scale change in a system called “critical transition” is viewed as a global bifurcation in the dynamics, and is studied by employing recent progress in the theory of dynamical systems such as topological computation theory and Morse decompositions. The obtained results are as follows: (1) The topological computation theory for obtaining the global structure of dynamics in the form of Morse decompositions from time-series data generated from dynamical systems is adapted for noisy time-series data, called the MGSTD method, which is successfully applied to meteorological time-series data capturing an expected transition of pressure patterns. (2) Discovery and analysis of a hysteresis-like “bifurcation” in hybrid systems which models analogue of the walk-run transition in the human bipedal locomotion. (3) Development of the method for obtaining Morse decomposition of the spacio-temporal dynamics from spatial image data by using the methods in the topological data analysis.
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| Free Research Field |
力学系理論
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| Academic Significance and Societal Importance of the Research Achievements |
臨界的遷移は大規模な災害や気候変動を予測し制御する上で重要な概念であるが，その根元的な理解は極めて不十分である．本研究では，その第１歩としての数理的な基礎研究を行い，力学系の大域的分岐理論がどのようにその理解に迫れるかに挑戦した．まだ決定的な理解には及ばないが，本研究で得られたMGSTD法は今後の実用研究にも活用できる可能性があると考えており，今後さらに研究を継続していく所存である．
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