Random dynamical systems approaches to noise-induced phenomena

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540390
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Hokkaido University
• Principal Investigator: SATO Yuzuru 北海道大学, 電子科学研究所, 准教授 (30342794)
• Co-Investigator(Kenkyū-buntansha): SUMI Hiroki 大阪大学, 理学研究科, 准教授 (40313324) ; YANO Koji 京都大学, 理学研究科, 准教授 (80467646)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ランダム力学系理論 / 雑音誘起現象 / 非線形時系列解析

Outline of Final Research Achievements

Recently multiple noise-induced transitions, statistical periodicity, noise-induced reproducibility has been discovered in a broad class of nonlinear dynamical systems. The goal of this research is to establish a theory of noise-induced phenomena and to analyze complex phenomena including stochastic chaos in random dynamical systems quantitatively. The following (1)-(3) are the main results of this research. (1) Universality of multiple noise-induced transitions, statistical periodicity,noise-induced reproducibility has been confirmed numerically. (2) Experimental time series analysis for human brain wave and dice roll, and their modeling with random dynamical systems have been studied. (3) Stochastic resonance and noise-induced chaos are formalized in terms of bifurcation theory. Statistical periodicity is analyzed in terms of ergodic theory.

Free Research Field

非線形動力学、複雑系