Signal propagation and failure in one-dimensional FitzHugh-Nagumo equations with periodic stimuli

We analyze the effect of additive periodic stimuli in one-dimensional FitzHugh-Nagumo equations in an excitable regime. With a suitable stimulus interval, the suppression of the pulse propagation occurs in some parameter regime. This propagation failure comes from the formation of the "death spot" where successive pulses annihilate. In the parameter regime where the solitary pulse cannot propagate in space stably, however, periodic stimuli cause a propagation of envelope of a traveling pulse under a "resonance" condition, i.e., the pulse at the leading edge disappears successively, however, an envelope is formed and propagates with keeping its shape.