Effects of surface size on minimalistic stochastic models for the catalytic CO oxidation

The impact of surface size on two minimalistic models for the bistable CO oxidation is analytically studied. A simple model for the catalytic CO oxidation on nanoscale surfaces is analyzed by the chemical master equation. The analytical results predict a shift of the bistable region and cusp point in the global bifurcation diagram as a function of surface size. A reaction-diffusion stochastic model consisting of a collection of reactive subdomains locally coupled by CO diffusion is also considered. A local description of fluctuations can be obtained after applying a Weiss-type mean-field approximation. This approximation predicts, for infinitely many subdomains, a break of ergodicity and a bifurcation behavior like in first-order phase transitions as a function of surface size and coupling parameter. Analytical results are compared with Gillespie-type Monte Carlo simulations.