Resonance and the Formation of Death-Spot in One-Dimensional FitzHugh-Nagumo Equations

We analyze the effect of periodic forcing on a chain of FitzHugh-Nagumo elements in an excitable regime. The element at the end of chain is coupled unidirectional to a single pacemaker, limit cycle oscillator. With a suitable pacemaker's frequency, we find that the suppression of the pulse propagation occurs in some parameter regime, while the isolated pulse propagates stably in the chain. This propagation failure comes from the formation of the "death-spot", where successive pulses annihilate.