Development and Application of Topological Computation Theory for Dynamical Systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 25287029
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Kyoto University
• Principal Investigator: Kokubu Hiroshi 京都大学, 理学研究科, 教授 (50202057)
• Co-Investigator(Renkei-kenkyūsha): HIRAOKA Yasuaki 東北大学, 材料科学高等研究所, 教授 (10432709) ; ARAI Zin 中部大学, 創発学術院, 教授 (80362432) ; TAKAHASHI Hiroki 慶応義塾大学, 理工学部, 准教授 (00467440) ; SAKAJO Takashi 京都大学, 大学院理学研究科, 教授 (10303603) ; MOCHIZUKI Atsushi 理化学研究所, 望月理論生物学研究室, 主任研究員 (10304726) ; INATSU Masaru 北海道大学, 理学研究院, 教授 (80422450)
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: 力学系 / トポロジー / 計算機援用解析 / 時系列 / 気象学 / 位相計算 / 生命科学 / ネットワーク

Outline of Final Research Achievements

Combining ideas and methods from Topology and Coputation, a new method, called the topological computation theory for global structures of dynamical systems, has been developed in order to give better understandings of dynamics appearing in various fields of Science and Technology. As its applications, studied are network dynamics such as the gene regulatory network in the Life Science, as well as the development of a new dynamical time-series analysis method which extracts information on underlying dynamics from noisy time-series data such as meteorological observation data.

Free Research Field

力学系理論