Frequency-selective induction of excitation waves near sub- and supercritical Hopf bifurcation

We study diffusively coupled excitable systems where local perturbations induces propagation waves only within finite frequency bands. Resonance-associated complex wave trains are found for parameters fixed near the subcritical Hopf bifurcation, and crisis-associated regular spiking near a supercritical Hopf bifurcation. Whereas in the subcritical case the qualitative excitation pattern of the coupled system is similar to that of an individual element, in the supercritical case the coupling works as a narrow band-pass filter for the external perturbation.