Spirals and heteroclinic cycles in a spatially extended Rock-Paper-Scissors model of cyclic dominance

Abstract

Spatially extended versions of the cyclic-dominance Rock-Paper-Scissors model have traveling wave (in one dimension) and spiral (in two dimensions) behavior. The far field of the spirals behave like traveling waves, which themselves have profiles reminiscent of heteroclinic cycles. We compute numerically a nonlinear dispersion relation between the wavelength and wavespeed of the traveling waves, and, together with insight from heteroclinic bifurcation theory and further numerical results from 2D simulations, we are able to make predictions about the overall structure and stability of spiral waves in 2D cyclic dominance models.