One-dimensional domains in systems with long-range inhibition

We investigate a standard model-sharing characteristic properties with the Van der Pol oscillator for electrical generators and the FitzHugh-Nagumo system. We study the effect of a long ranging inhibitor and discuss the behaviour of solutions at short and large length scales. The main result is the existence of two inhomogeneous solutions—the smaller one is always a saddle corresponding to a critical nucleus; the larger one appears stable for overcritical coupling.