Characterization of spiraling patterns in spatial rock-paper-scissors games
arXiv:1407.0621 · doi:10.1103/PhysRevE.90.032704
Abstract
The spatio-temporal arrangement of interacting populations often influences the maintenance of species diversity and is a subject of intense research. Here, we study the spatio-temporal patterns arising from the cyclic competition between three species in two dimensions. Inspired by recent experiments, we consider a generic metapopulation model comprising "rock-paper-scissors" interactions via dominance removal and replacement, reproduction, mutations, pair-exchange and hopping of individuals. By combining analytical and numerical methods, we obtain the model's phase diagram near its Hopf bifurcation and quantitatively characterize the properties of the spiraling patterns arising in each phase. The phases characterizing the cyclic competition away far from the Hopf bifurcation (at low mutation rate) are also investigated. Our analytical approach relies on the careful analysis of the properties of the complex Ginzburg-Landau equation derived through a controlled (perturbative) multiscale expansion around the model's Hopf bifurcation. Our results allows us to clarify when spatial "rock-paper-scissors" competition leads to stable spiral waves and under which circumstances they are influenced by nonlinear mobility.
16 two-column pages, 16 figures
References in corpus (15)
- Evolutionary games on graphs
- Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
- Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
- Noise and Correlations in a Spatial Population Model with Cyclic Competition
- Self-Organization of Mobile Populations in Cyclic Competition
- Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations
- Zero-one survival behavior of cyclically competing species
- Quasi-cycles in a spatial predator-prey model
- Instability of spatial patterns and its ambiguous impact on species diversity
- Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates
- Effects of competition on pattern formation in the rock-paper-scissors game
- Influence of local carrying capacity restrictions on stochastic predator-prey models
- Emergence of target waves in paced populations of cyclically competing species
- Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
- Evolutionary games on minimally structured populations