Catalytic oscillators are usually characterized by dynamic variables that cannot be perturbed directly, by wide separation of time scales and by either soft or hard bifurcation to periodicity. Analysis of a simple relaxation oscillator subject to a square-wave variation in a parameter reveals a structure similar to that known for the circle map. Qualitative analysis of periodic forcing around a hard-bifurcation boundary is also presented. These results are compared with motions obtained by a periodic change in the composition of the environment surrounding a Pt wire catalyzing NH3 oxidation. The unperturbed system exhibits the three features described above. Harmonic quasiperiods and narrow subharmonic bands are mapped in the forced system.