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Bifurcation and resonance in a fractional Mathieu-Duffing oscillator

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  • J.H. Yang
  • Miguel A.F. Sanjuán
  • H.G. Liu

Abstract

The bifurcation and resonance phenomena are investigated in a fractional Mathieu-Duffing oscillator which contains a fast parametric excitation and a slow external excitation. We extend the method of direct partition of motions to evaluate the response for the parametrically excited system. Besides, we propose a numerical method to simulate different types of local bifurcation of the equilibria. For the nonlinear dynamical behaviors of the considered system, the linear stiffness coefficient is a key factor which influences the resonance phenomenon directly. Moreover, the fractional-order damping brings some new results that are different from the corresponding results in the ordinary Mathieu-Duffing oscillator. Especially, the resonance pattern, the resonance frequency and the resonance magnitude depend on the value of the fractional-order closely. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • J.H. Yang & Miguel A.F. Sanjuán & H.G. Liu, 2015. "Bifurcation and resonance in a fractional Mathieu-Duffing oscillator," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(11), pages 1-8, November.
    • Handle: RePEc:spr:eurphb:v:88:y:2015:i:11:p:1-8:10.1140/epjb/e2015-60315-y
    DOI: 10.1140/epjb/e2015-60315-y
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    Statistical and Nonlinear Physics;

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