A LOTKA-TYPE MODEL FOR OSCILLATIONS IN SURFACE-REACTIONS

In this paper we introduce a reaction model on a lattice which leads t o oscillations. The model consists of two monomolecular and one bimole cular reaction step and is related to the Lotka model. Despite the sim ple evolution rules, the model shows a complex behaviour (i.e. the app earance of oscillations). This offers us the opportunity to test diffe rent types of stochastic approximations and compare them with the resu lts of a Monte Carlo simulation. The simulation is performed on a larg e lattice (L = 1024) in order to take long-range correlations into acc ount. Comparing the results of this simulation with the stochastic app roaches shows that only advanced numerical approximations are able to predict the system behaviour correctly. Simple approximations which do not account for long-range correlations (such as mean-field approxima tions) fail in the prediction of the system behaviour. The correlation analysis (an advanced stochastic description) is in overall good agre ement with the results of the simulation and therefore is an alternati ve to computer simulation. Moreover, it is not restricted to using a f inite lattice and does not need a large amount of computing time.