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The pitchfork bifurcation and vibrational resonance in a quintic oscillator

Yang Jian-Hua Liu Hou-Guang Cheng Gang

The pitchfork bifurcation and vibrational resonance in a quintic oscillator

Yang Jian-Hua, Liu Hou-Guang, Cheng Gang
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  • Abstract views:  788
  • PDF Downloads:  478
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Publishing process
  • Received Date:  08 May 2013
  • Accepted Date:  06 June 2013
  • Published Online:  05 September 2013

The pitchfork bifurcation and vibrational resonance in a quintic oscillator

  • 1. School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China
Fund Project:  Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2012QNA21) and the Priority Academic Program Development of Jiangsu Higher Education Institutions, China.

Abstract: The pitchfork bifurcation and vibrational resonance are investigated in this paper. Based on the method of separating slow motion from fast motion, the equivalent equation to the slow motion is obtained. Then, the pitchfork bifurcation is studied. The results show that the amplitude of the high-frequency signal can induce the subcritical pitchfork bifurcation, while both the frequency of the high-frequency signal and the value of the fractional-order can induce supercritical pitchfork bifurcation. The pattern of the vibrational resonance depends on the pitchfork bifurcation. The vibrational resonance presents double-resonance pattern when the pitchfork bifurcation occurs. Or else, the vibrational resonance presents single-resonance pattern. The analytical predications are in good agreement with the numerical calculation results, which verifies the validity of the theoretical results.

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