| Project/Area Number |
16KT0138
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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 | 特設分野 |
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| Research Field |
Mathematical Sciences in Search of New Cooperation
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| Research Institution | Ryukoku University |
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Principal Investigator |
Oka Hiroe 龍谷大学, 理工学部, 教授 (20215221)
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| Project Period (FY) |
2016-07-19 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 力学系 / 制御ネットワーク / 大域的構造 / モース分解 / Conley index / 時系列解析 / 不安定ダイナミクス / switching system / ネットワーク結合系 / 位相的計算理論 |
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| Outline of Final Research Achievements |
(A) Topological and computational method for dynamical systems is a computer-assisted method developed by the people including the author,in order to analyze the global structures of the dynamical systems and its bifurcations. From time series data obtained by complex network systems like gene regulatory networks, the author formulate the theory for reconstructing the global structure of the systems like Morsedecomposition and also did some computation for Mirsky’s model for circadian rhythms.
(B) In this project we apply this method to the switching systems which is one of the coupled neural regulatory networks of biomolecules, and give the mathematical formulation.
(C) We compute the persistence diagram form the time series data of the vector field of 3-dimensional turbulence, and obtain some characteristic structure.
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| Academic Significance and Societal Importance of the Research Achievements |
研究代表者はこれまで, 分岐理論を用いた解析的アプローチやConley 指数などの力学系の位相不変量を用いたトポロジー的アプローチによる研究を行い, ホモロジー計算などの位相的方法に精度保証付き数値計算を組み合わせ、数学的に厳密で汎用性のあるアルゴリズムの構築を試みてきた．この方法をswitchig systemsと言われる生体分子の制御ネットワーク結合系に適用し、遺伝子ネットワークなどの生物学的研究に新しい方法を与えることができる。また, この手法は, 力学系の枠組みの新しい視点を構築し, 数学的な新規性についても寄与している.
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