Generalized stochastic resonance of power function type single-well system

Abstract

To generalize the harmonic potential of the linear random vibration system, a more general power type potential is presented, and the corresponding power function type nonlinear single-well random vibration system is obtained. The first moment of the system steady-state response and the stationary variance of the system response, which are influenced by noise strength, parameters of the potential and the periodic excitation, are studied by using the second order stochastic Runge-Kutta algorithm. The parameter b, which determines the shape of the potential, goes through b b > 2 and b=2 (harmonic potential), and it is shown that varying the noise strength, if b b=2 (harmonic potential) or b > 2, this phenomenon does not occur; varying the parameters of the potential, the first moment of the system steady-state response and the stationary variance of the system response can also be non-monotonic.