Alternative stable rotors in an excitable medium

Abstract

A given excitable medium (continuous, uniform, isotropic, simply connected, two- or three-dimensional) may support alternative types of vortex-like solution radiating from a ‘rotor’. These have distinct periods, wavelengths, behaviors near interfaces, and, in rotationally symmetric vortex rings, different contraction or expansion rates and drift rates. Initial conditions select among the discrete alternatives. Rotors of different types may coexist within one medium, until the interface between their domains encroaches upon the rotor of longer period. Examples are given using the FitzHugh-Nagumo model. They are interpreted in terms of the measured dispersion curve for one-dimensional propagation and a hypothetical ‘curvature relation’ with one undetermined parameter.