A surface reaction model for the catalyzed reaction A +(1/2)B-2-->AB is studied by means of Monte Carlo simulations. Motivated by experiments on the catalytic oxidation of CO on certain Pt surfaces; i.e., A=CO, B-2=O-2, and AB=CO2; it is assumed that the catalyst surface undergoes reactant's induced reversible phase transitions (RIRPT's) between two different structures, i.e., a stable (reconstructed) phase in the low (high) A-coverage regime. Also the sticking coefficient of B-2-species depends on the surface structure, being negligible in the stable phase. Two cases are studied in detail depending on whether the RIRPT's involve the whole surface and are due to the average coverage of the sample or, on the other hand, they are restricted to small patches of the surface and are driven by the local coverage. For the case of global RIRPT's, the reactive regime of the system exhibits self-sustained oscillatory behavior. However, considering local RIRPT's oscillations are observed in finite samples but it is shown that they will vanish in the thermodynamic limit.