ABSTRACT Here we provide a detailed comparison of three different treatments of the monomer-dimer (or A+B2) surface reaction. The traditional mean-field (MF) treatment is well known to produce bistability, disappearing at a cusp bifurcation, as the desorption rate for A increases. Additional MF reaction-diffusion equations studies of propagation of chemical wave fronts separating the stable states allow determination of equistability. This facilitates a natural comparison with recent lattice-gas (LG) treatments which reveal non-equilibrium discontinuous traditions and critical points. The effect of fluctuations on metastability, nucleation, wave propagation, and critical behavior in the LG model are also discussed. We also present a hybrid treatment using a MF (LG) description adsorbed A (B) which is assumed highly mobile (relatively immobile). Here one finds MF-type bistability together with LG-type continuous B-poisoning transitions. This behavior is elucidated. A variety of extensions of the basic A+B2 model are also described.
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