Open AccessComplicated behaviors and non-smooth bifurcation of a switching system with piecewise linearchaotic circuit
Author(s) -
Lifeng Wu,
Yong Guan,
Yong Liu
Publication year - 2013
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.62.110510
Subject(s) - period doubling bifurcation , bifurcation , biological applications of bifurcation theory , saddle node bifurcation , chaotic , piecewise linear function , bifurcation diagram , transcritical bifurcation , bogdanov–takens bifurcation , piecewise , electronic circuit , mathematics , pitchfork bifurcation , mathematical analysis , control theory (sociology) , hopf bifurcation , nonlinear system , physics , computer science , quantum mechanics , control (management) , artificial intelligence
The complex dynamical and non-smooth bifurcations of a compound system with periodic switches between two piecewise linear chaotic circuits are investigated. Based on the analysis of equilibrium states, the conditions for Fold bifurcation and Hopf bifurcation are derived to explore the bifurcations of the compound system with periodic switches while there are different stable solutions in the two subsystems. Different types of oscillations of the swithing system are observed, and the mechanism is studied and presented. In the difference of periodic oscillations, the number of the swithing points increases doubly with the variation of the parameter, which leads from period-doubling bifurcation to chaos.