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A Lotka-type model for oscillations in surface reactions

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In this paper we introduce a reaction model on a lattice which leads to oscillations. The model consists of two monomolecular and one bimolecular reaction step and is related to the Lotka model. Despite the simple evolution rules, the model shows a complex behaviour (i.e. the appearance of oscillations). This offers us the opportunity to test different types of stochastic approximations and compare them with the results of a Monte Carlo simulation. The simulation is performed on a large lattice (L = 1024) in order to take long-range correlations into account. Comparing the results of this simulation with the stochastic approaches 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 approximations) fail in the prediction of the system behaviour. The correlation analysis (an advanced stochastic description) is in overall good agreement with the results of the simulation and therefore is an alternative to computer simulation. Moreover, it is not restricted to using a finite lattice and does not need a large amount of computing time.