Monte Carlo and numerical studies of coloured noise and stochastic resonance problems

We suggest two algorithms for evaluating dynamical systems described as first order differential equations under the influence of external noise represented by an Ornstein-Uhlenbeck process: a direct Monte Carlo simulation of the equation of motion and a numerical integration of the associated composite marcov equation. The two algorithms complement one another with respect to small and large noise correlation times and produce results which agree within any desired accuracy. We apply our algorithms to the problem of stochastic resonance and present the numerical results of first passage time densities, transition rates und phase histograms as functions of the system parameters frequency of the periodic force, noise correlation time and noise strength.