Abstract

Slow variables are added to account for the order difference between the excitation frequency and the natural frequency in order to turn this model into a fast-slow model. Under various excitation frequencies and amplitudes, the dynamic equations are obtained. When the equilibrium point is unstable, bifurcation theory is used to analyze bifurcation action, and the conditions for creating a folding bifurcation are extracted. The effect of excitation frequency and amplitude on dynamic behavior is investigated numerically using the curve of the equilibrium point, transformed phase portrait, and time course.

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