Toward a new approach to transient dynamics

2014 Fiscal Year Final Research Report

• Project/Area Number: 23684002
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Hokkaido University
• Principal Investigator: ARAI Zin 北海道大学, 理学(系)研究科(研究院), 准教授 (80362432)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 応用数学 / アルゴリズム / 力学系 / カオス

Outline of Final Research Achievements

For the study of transient behaviors of dynamical systems on non-invariant set such as transient chaos, we develop a numerical method based on graph clustering algorithms. We also develop an algorithm to construct pseudo-Lyapunov functions, an analog of Lyapunov function, based on optimization algorithms. This enables us to study a generalization of Conley-Morse decomposition to dynamical systems having no Lyapunov function. These algorithms are successfully applied to dynamical systems including non-linear Leslie model and also to numerical simulations of 2-dimensional fluid flows.

Free Research Field

数学