  The effects of a spatially periodic forcing on an oscillating chemical
reaction as described by the Lengyel-Epstein model are investigated. We find a
surprising competition between two oscillating patterns, where one is harmonic
and the other subharmonic with respect to the spatially periodic forcing. The
occurrence of a subharmonic pattern is remarkable as well as its preference up
to rather large values of the modulation amplitude. For small modulation
amplitudes we derive from the model system a generic equation for the envelope
of the oscillating reaction that includes an additional forcing contribution,
compared to the amplitude equations known from previous studies in other
systems. The analysis of this amplitude equation allows the derivation of
analytical expressions even for the forcing corrections to the threshold and to
the oscillation frequency, which are in a wide range of parameters in good
agreement with the numerical analysis of the complete reaction equations. In
the nonlinear regime beyond threshold, the subharmonic solutions exist in a
finite range of the control parameter that has been determined by solving the
reaction equations numerically for various sets of parameters.
