Frequency-resonance-enhanced vibrational resonance in bistable systems

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Abstract
The dynamics in an overdamped bistable system subject to the action of two periodic forces (assuming their frequencies are $\omega${} and $\Omega${}, and amplitudes are A and B, respectively) is studied. For the usual vibrational resonance, the nonmonotonic dependence of signal output of the low frequency $\omega${} on the change of B for a fixed $\Omega${}, the condition $\Omega${}$\gg${}$\omega${} 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 $\Omega${} and amplitude B. Especially, the resonance becomes stronger when $\Omega${} is chosen such that it is exactly in frequency resonance with $\omega${}. 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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