A general scheme for studying the stochastic dynamics of a parametric oscillator driven by coloured noise

Abstract

The stochastic dynamics of a classical parametric oscillator driven by coloured noise with exponential correlation is studied both by analytical and numerical methods. The critical strength of the parametric modulation at which the motion of the oscillator becomes unbounded, and the dependence of this critical strength on the magnitude and the correlation length of the noise, are investigated. The results show that the critical strength does not depend on either the strength or the correlation length of the coloured noise, but that the squeezing induced by the parametric oscillation is enhanced by increasing the correlation length of the noise.