Open AccessOscillations and their mechanism of compound system with periodic switches between two subsystems
Author(s) -
Yue Yu,
Chun Zhang,
Xiujing Han,
Qinsheng Bi
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.200507
Subject(s) - period doubling bifurcation , bifurcation , chaotic , nonlinear system , control theory (sociology) , hopf bifurcation , mechanism (biology) , biological applications of bifurcation theory , topology (electrical circuits) , mathematics , computer science , physics , quantum mechanics , combinatorics , control (management) , artificial intelligence
Complicated behaviors of the compound system with periodic switches between two nonlinear systems are investigated in detail. Through the local analysis, the critical conditions such as fold bifurcation and Hopf bifurcation are derived to explore the bifurcations of the compound systems with different stable solutions in the two subsystems. Different types of oscillations of the switched system are observed of which, the mechanism is presented to show that the trajectories of the oscillations can be divided into several parts by the switching points, governed by the two subsystems, respectively. With the variation of the parameters, cascading of doubling increase of the switching points can be obtained, leading to chaos via period-doubling bifurcations. Furthermore, because of the non-smooth characteristics at the switching points, different forms of bifurcations may occur in the compound system, which may result in complicated dynamics such as chaotic oscillations, instead of the simple connections between the trajectories of the two subsystems.