A pedestrian approach to transitions and fluctuations in simple nonequilibrium chemical systems

Abstract

A method is presented for identifying the quasi-stable states of a simple class of spatially homogeneous, nonlinear, nonequilibrium chemical systems, and for numerically calculating the associated mean transition times, mean fluctuation periods and effective fluctuation ranges. The method of analysis is based on a “stochastic simulation” approach instead of a “master equation” approach, and it therefore focuses on the behavior of a typical individual system instead of on the collective behavior of a statistical ensemble of systems. Results of explicit calculations are presented for a model set of reactions proposed by Schlögl, and some clarification is achieved regarding hysteresis effects and the effects of an absorbing null state.