Bifurcation and resonance in a fractional Mathieu-Duffing oscillator

J.H. Yang (), Miguel A.F. Sanjuán and H.G. Liu

The European Physical Journal B: Condensed Matter and Complex Systems, 2015, vol. 88, issue 11, 1-8

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

Keywords: Statistical and Nonlinear Physics (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1140/epjb/e2015-60315-y

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