Coarse bifurcation analysis of kinetic Monte Carlo simulations: A lattice-gas model with lateral interactions

We present a computer-assisted study of ‘‘coarse’’ stability/bifurcation calculations for kinetic Monte Carlo simulators using the so-called coarse timestepper approach presented in A. G. Makeev, D. Maroudas, and I. G. Kevrekidis, J. Chem. Phys. 116, 10083 ~2002!. Our illustrative example is a model of a heterogeneous catalytic surface reaction with repulsive adsorbate–adsorbate interactions and fast diffusion. Through numerical continuation and stability analysis, we construct oneand two-parameter coarse bifurcation diagrams. We also discuss several computational issues that arise in the process, the most important of which is the ‘‘lifting’’ of coarse, macroscopic initial conditions ~moments of adsorbate distributions! to fine, microscopic initial conditions ~distributions conditioned on these moments!. © 2002 American Institute of Physics. @DOI: 10.1063/1.1512274#