Master equation simulations of a model of a thermochemical system

Master equation approach is used to study the influence of fluctuations on the dynamics of a model thermochemical system. For appropriate values of parameters, the deterministic description of the system gives the subcritical or supercritical Hopf bifurcations. For small systems (containing 100 000 particles) close to the supercritical Hopf bifurcation, the stochastic trajectories obtained from numerical simulations do not allow to distinguish between damped oscillations around a stable focus and sustained oscillations around a small stable limit cycle. This uncertainty disappears if the number of particles in the system is increased (up to 1 000 000). Close to subcritical Hopf bifurcation the stochastic trajectory of the system jumps from the basin of attraction of a stable focus to the basin of attraction of a stable limit cycle. In this case the time dependencies of temperature and concentration of reactant in the system are apparently similar to intermittent chaotic oscillations. The mean first passage time for the transitions from the stable focus to the stable limit cycle show the characteristic exponential dependence on the number of particles. This passage time depends very strongly on the bifurcation parameter (reaction heat), which determines the distance between the stable focus and an unstable limit cycle.