Open AccessBifurcation and chaos of some relative rotation system with triple-well Mathieu-Duffing oscillator
Author(s) -
Bin Liu,
Zhao Hong-xu,
Hou Dong-Xiao
Publication year - 2014
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.63.174502
Subject(s) - bifurcation , duffing equation , nonlinear system , physics , singularity , mathieu function , mathematical analysis , classical mechanics , mathematics , quantum mechanics
The dynamic equation of a nonlinear relative rotation system with a triple-well Mathieu-Duffing oscillator is investigated. Firstly, a codimension three-bifurcation characteristic is deduced by combining with the multi-scale method and singularity theory under the condition of nonautonomy. Secondly, the threshold value of chaos about Smale horseshoe commutation is given from Melnikov method. Finally, the numerical simulation exhibits safe basins and chaos, and the erosion process of safe basins, which is closely related to the process, leading to chaos.