Fast-slow analysis for parametrically and externally excited systems with two slow rationally related excitation frequencies

作     者：Xiujing Han Qinsheng Bi Peng Ji Jürgen Kurths 

作者机构：Faculty of Civil Engineering and Mechanics Jiangsu University Zhenjiang Jiangsu 212013 People's Republic of China Potsdam Institute for Climate Impact Research Potsdam 14473 Germany Department of Physics Humboldt University Berlin 12489 Germany Institute for Complex Systems and Mathematical Biology University of Aberdeen Aberdeen AB24 3UE United Kingdom Department of Control Theory Nizhny Novgorod State University Gagarin Avenue 23 606950 Nizhny Novgorod Russia 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2015年第92卷第1期

页      面：012911-012911页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

基　　金：National Natural Science Foundation of China [11202085, 21276115, 11302087, 11302086, 11402226] Natural Science Foundation of Jiangsu Province [BK20130479] Research Foundation for Advanced Talents of Jiangsu University [11JDG075] 

主　　题：OSCILLATIONS RESEARCH DYNAMICAL systems HOPF bifurcations FREQUENCIES of oscillating systems VAN der Pol oscillators (Physics) DUFFING oscillators EXCITATION spectrum 

摘      要：We present a general method for analyzing mixed-mode oscillations (MMOs) in parametrically and externally excited systems with two low excitation frequencies (PEESTLEFs) for the case of arbitrary m:n relation between the slow frequencies of excitations. The validity of the approach has been demonstrated using the equations of Duffing and van der Pol, separately. Our study shows that, by introducing a slow variable and finding the relation between the slow variable and the slow excitations, PEESTLEFs can be transformed into a fast-slow form with a single slow variable and therefore MMOs observed in PEESTLEFs can be understood by the classical machinery of fast subsystem analysis of the transformed fast-slow system.