A lattice gas model for the catalyzed reaction A + 1/2B(2) --> AB is studied. Motivated from experiments on the catalytic oxidation of CO on Pt surfaces, it is assumed that the catalyst surface undergoes reactant-induced reversible phase transitions between two different structures, i.e., a stable (reconstructed) phase in the low (high) A coverage limit. Also the sticking coefficient of B-2 species depends on the surface structure, being negligible in the stable phase. For low pressures of A species the systems have a reactive regime, while increasing such pressure a first-order irreversible phase transition onto an A poisoned state is observed. The structural transitions of the surface coupled with reactant coverages causes an oscillatory behavior in the reactive regime of the reaction. Away from the critical point, oscillations are periodic; however, close to criticality the onset of no-periodic oscillations is observed. Also, on approaching criticality the average period of the A rich phase diverges algebraically with exponent eta = 1, in agreement with the fact that just at the critical edge and in the t --> infinity limit the surface will be fully covered with A species.