Stochastic resonance of an underdamped linear harmonic oscillator with fluctuating mass and fluctuating frequency

Abstract

When Brownian particle moves in a viscoelastic medium, the surrounding molecules not only collide with the Brownian particle but also adhere to the Brownian particle randomly, thereby changing the mass of the Brownian particle. We investigate the stochastic resonance phenomenon in an underdamped linear harmonic oscillator with fluctuating mass and fluctuating frequency under an external periodic force. The exact expressions of the first moment and the amplitude of the output signal are obtained by using the Shapiro-Loginov formula and the Laplace transform technique. We establish the necessary and sufficient conditions for the emergence of the stochastic resonance phenomenon induced by the mass fluctuation noise intensity and frequency fluctuation noise intensity. Furthermore, based on the necessary and sufficient conditions, the output amplitude shows a non-monotonic dependence on the noise intensity, which means that the stochastic resonance phenomenon happens.