The effects of low-dimensional supports (one and two dimensions) on the steady state and the dynamics of open reactive systems capable of giving rise to oscillatory behavior are studied. A lattice Lotka-Volterra model involving reaction, adsorption, and desorption mechanisms is developed for which mean-field behavior predicts a continuum of closed trajectories around a center. It is shown that the spatial constraints of the support radically change this behavior. Specifically, while in one dimension, oscillations are suppressed, in two dimensions, the system selects a preferred oscillation frequency depending on the intrinsic parameters and the lattice geometry.