Abstract: The game of Rock-Paper-Scissors is an archetype for cyclic competition that occurs in ecosystems in the natural world. The well mixed stochastic process is modelled by the well known May-Leonard mean-field rate equations, which contain a heteroclinic cycle. When the populations depend on space, the rate equations are augmented by diffusion, and simulations of the equations readily produce travelling waves in one dimension and spiral waves in two, in which waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. In this talk I will discuss how the heteroclinic cycle in the May-Leonard equations can inform the understanding of the existence of the travelling waves, and the relationship between rotation rate and far-field wavelength of the spirals.

Reference: C. M. Postlethwaite and A. M. Rucklidge, EPL, 117 (2017) 48006  http://dx.doi.org/10.1209/0295-5075/117/48006