Resonance in periodically inhibited reaction–diffusion systems

We have conducted experiments on a periodically inhibited oscillatory Belousov–Zhabotinsky (BZ) reaction–diffusion system in a regime in which the patterns oscillate at half the frequency of the forcing (the 2:1 resonance regime). The periodic perturbations of the photosensitive (ruthenium-catalyzed) reaction are made with light, which inhibits the oscillatory behavior. Increasing the light intensity increases the refractory period (time for recovery from inhibition), which decreases the oscillation frequency of the patterns in the medium. We investigate the behavior for two different levels of inhibitor concentration in the reagent feed to determine the shape of the 2:1 resonant regime as a function of the forcing intensity and forcing frequency. At high forcing intensity, the inhibition leads to a transition from traveling waves (spirals) to standing waves. Simulations of a reaction–diffusion model with FitzHugh–Nagumo kinetics yield behavior similar to that observed in the experiments.