Open AccessAnalysis of bifurcation and chaos in a class of piecewise smooth systems based on symbolic sequence
Author(s) -
Ming Li,
Xikui Ma,
Dong Dai,
Hao Zhang
Publication year - 2005
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.54.1084
Subject(s) - bifurcation , piecewise , saddle node bifurcation , period doubling bifurcation , mathematics , nonlinear system , homoclinic bifurcation , bifurcation diagram , biological applications of bifurcation theory , topology (electrical circuits) , sequence (biology) , control theory (sociology) , mathematical analysis , physics , computer science , combinatorics , artificial intelligence , control (management) , quantum mechanics , biology , genetics
Based on the sequence of circuit topologies, a symbolic sequence method is proposed for analyzing the bifurcations and chaos in a class of piecewise smooth systems like DC/DC converters. The largest subsequence(LS) is used to distinguish the type of bifurcation and detect border collision bifurcation e. g., when a perioddoubling bifurcation occurs, the LS is unchanged; when border collision bifurcation occurs, the LS is changed; and when chaos occurs,the LS does not exist.It is shown that the duty ratio is an essential variable for describing the nonlinear dynamics of a class of piecewise smooth systems like DC/DC converters and saturating nonlinearity is the root cause of border collision bifurcation.