Cycling behaviour and spatial structure in a heteroclinic network model of Rock-Paper-Scissors-Lizard-Spock #

Alastair M Rucklidge

10:50 Wednesday in 4Q04.

Part of the Nonlinear dynamics and applications session.

Abstract #

The well-known game of Rock-Paper-Scissors can be used as a simple model of competition between three species. When modelled in continuous time using ordinary differential equations, the resulting system contains a heteroclinic cycle between the three equilibrium solutions that represent the existence of only a single species. The game can be extended in a symmetric fashion by the addition of two further strategies (Lizard' and Spock’): now each strategy is dominant over two of the other four strategies, and is dominated by the remaining two. The ODE model contains coupled heteroclinic cycles forming a heteroclinic network. We develop a technique, based on the concept of fragmentary asymptotic stability, to understand the stability of arbitrarily long periodic sequences of visits made to the neighbourhoods of the equilibria. The regions of stability form a complicated pattern in parameter space. By adding spatial diffusion, we extend to a partial differential equation model and investigate the spatiotemporal evolution of these periodic itineraries.