Stochastic resonance of a damped linear oscillator

The stochastic resonance is studied for a damped linear oscillator subject to both parametric excitation of random noise and external excitation of periodically modulated random noise. By means of the Shapiro-Loginov formula, the expressions of the first-order and the second-order moments are obtained for the system response. It is found that there exist conventional stochastic resonance, bona fide stochastic resonance and stochastic resonance in a broad sense in the system. When the noise intensity ratio R≥1, the stochastic multi-resonance is found in the system. Moreover, the numerical results of power spectrum density of system response are presented to verify the analytic results.