Frequency-resonance-enhanced vibrational resonance in bistable systems

Abstract

The dynamics in an overdamped bistable system subject to the action of two periodic forces (assuming their frequencies are ω and Ω, and amplitudes are A and B, respectively) is studied. For the usual vibrational resonance, the nonmonotonic dependence of signal output of the low frequency ω on the change of B for a fixed Ω, the condition Ω≫ω is always assumed in all previous studies. Here, removing this restriction, we find that a resonant behavior can extensively occur with respect to the changes of both the frequency Ω and amplitude B. Especially, the resonance becomes stronger when Ω is chosen such that it is exactly in frequency resonance with ω. This combinative behavior, called frequency-resonance-enhanced vibrational resonance, is of great interest and may shed an improved light on our understanding of the dynamics of nonlinear systems subject to a biharmonic force.

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