COMPARISON OF DETERMINISTIC AND STOCHASTIC KINETICS FOR NONLINEAR-SYSTEMS

The deterministic kinetics of chemical reactions is compared with a stochastic description for the cubic Schlogl model with a single stable steady state, which has a nonlinear reaction mechanism. We solve numerically the birth-death master equation for this system for various numbers of particles (N = 20-160). For small systems with tens of particles the deviation of the first moment of the stochastic distribution from the deterministic temporal variation of concentration can be substantial in the initial relaxation towards a stationary state. The relaxation of the master equation is faster than that of the deterministic equation. The maximum deviation in trajectories decreases as the parameters in the kinetic model are altered towards a linear mechanism. The maximum deviation differs from N 1/2 as N decreases, but approaches N 1/2 as N increases. Deviations from deterministic temporal evolution due to fluctuations depend on the extent of nonlinearity of the reaction. The variance of a stationary distribution of the master equation is shown to be significantly larger than the average for a nonlinear system.