Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance (SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory (LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density (PSD) and signal-to-noise ratio (SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.