The development of the topological and computational methods on dynamical systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540222
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Ryukoku University
• Principal Investigator: Oka Hiroe (國府宏枝) 龍谷大学, 理工学部, 教授 (20215221)
• Co-Investigator(Renkei-kenkyūsha): KOKUBU Hiroshi 京都大学, 大学院理学研究科, 教授 (50202057) ; ARAI Jin 北海道大学, 理学系研究科, 准教授 (80362432)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 力学系 / モース分解 / 大域的構造 / 時系列 / 全構造計算

Outline of Final Research Achievements

Topological-computational method (database schema) is our original approach in order to overcome the weak point of the analysis of real dynamical systems. The theory and an application (2-dim’l discrete dynamical system called Leslie model) is discussed in our paper. Also, boundary crisis, which is typical in the global bifurcations is studied in this methods, and obtain a theorem using a notion of chain orbit.
A switching network is a simple model for gene regulatory network representing the regulation of proteins, and we study the database of such systems. Moreover we treat the time series data of some gene regulatory network, from which we obtain a Morse decomposition, which is same as the one from a different method. We also study the graphical time series obtained by 3-D turbulence and get some computational results wrt persistence homology.

Free Research Field

力学系理論