Stochastic dynamics of a bistable reaction system

The method of stochastic dynamics is used for the study of a discrete trimolecular chemical model with internal fluctuations. Several trajectories of the phase point are simulated for the bistable Schlögl model at small volumes. The influence due to the discontinuity of the process on the stationary probability distribution function is analyzed. The transition to the bimodal distribution is shown to be a cusp catastrophe. The location of the cuspoid strongly depends on the reaction volume. Autocorrelation functions are calculated numerically for short and large time scales.