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Bifurcation and chaos of some relative rotation system with triple-well Mathieu-Duffing oscillator

Liu Bin Zhao Hong-Xu Hou Dong-Xiao

Bifurcation and chaos of some relative rotation system with triple-well Mathieu-Duffing oscillator

Liu Bin, Zhao Hong-Xu, Hou Dong-Xiao
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  • Abstract views:  773
  • PDF Downloads:  401
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Publishing process
  • Received Date:  25 February 2014
  • Accepted Date:  11 April 2014
  • Published Online:  05 September 2014

Bifurcation and chaos of some relative rotation system with triple-well Mathieu-Duffing oscillator

  • 1. College of Electrical Engineering, YanShan University, Qinhuangdao 066004, China;
  • 2. Department of Control Engineering Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 51405068, 51105324), the Natural Science Foundation of Hebei Province, China (Grant Nos. E2014501006, E2012203194), the Hebei Province Science and Technology Support Program (Grant No. 13211907D), and the Colleges and Universities Research Fund of Hebei Province (Grant No. ZD2014202).

Abstract: 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.

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