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

TL;DR

This paper investigates spiral and heteroclinic wave patterns in a spatially extended Rock-Paper-Scissors model, combining numerical analysis and bifurcation theory to understand their structure and stability.

Contribution

It provides the first detailed numerical and theoretical analysis linking heteroclinic cycles to spiral wave behavior in a spatial cyclic dominance model.

Findings

Computed nonlinear dispersion relation for traveling waves

Predicted stability conditions for spiral waves in 2D

Linked heteroclinic bifurcations to spiral wave dynamics

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.