A simple lattice gas model is studied for the description of the kinetic oscillations in the CO oxidation on the Pt(100) and Pt(110) surfaces. It takes CO diffusion and surface reconstruction into account and exhibits very interesting phenomena such as synchronized oscillations and mesoscopic pattern formation. The model uses only few parameters, the CO gas phase concentration y, the CO diffusion constant D, the surface phase propagation velocity V, and the ratio of the O-2 sticking coefficients on the two surface phases. This enables the study of the whole parameter regime and the theoretical stability analysis for the kinetic oscillations. It can be shown that it is only the ratio of the O-2 sticking coefficients on the reconstructed and non-reconstructed surfaces which determines the type of oscillations and the parameter range where these oscillations exist.