Frequency-resonance-enhanced vibrational resonance in bistable systems

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 >> 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.