Coexistence in a One-Dimensional Cyclic Dominance Process
arXiv:1006.0383 · doi:10.1103/PhysRevE.81.060901
Abstract
Cyclic (rock-paper-scissors-type) population models serve to mimic complex species interactions. Focusing on a paradigmatic three-species model with mutations in one dimension, we observe an interplay between equilibrium and non-equilibrium processes in the stationary state. We exploit these insights to obtain asymptotically exact descriptions of the emerging reactive steady state in the regimes of high and low mutation rates. The results are compared to stochastic lattice simulations. Our methods and findings are potentially relevant for the spatio-temporal evolution of other non-equilibrium stochastic processes.
4 pages, 4 figures and 2 pages of Supplementary Material. To appear in Physical Review E
References in corpus (8)
- Statistical physics of social dynamics
- Evolutionary games on graphs
- Theory of Phase Ordering Kinetics
- Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
- Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
- Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
- Spatial organization in cyclic Lotka-Volterra systems
- Stochastic Ballistic Annihilation and Coalescence
Cited by in corpus (14)
- Stochastic population dynamics in spatially extended predator-prey systems
- Effects of competition on pattern formation in the rock-paper-scissors game
- Cyclic competition of four species: domains and interfaces
- Interplay between partnership formation and competition in generalized May-Leonard games
- Global attractors and extinction dynamics of cyclically competing species
- Cyclic competition of four species: mean field theory and stochastic evolution
- Cyclic game dynamics driven by iterated reasoning
- Saddles, Arrows, and Spirals: Deterministic Trajectories in Cyclic Competition of Four Species
- A theoretical approach to understand spatial organization in complex ecologies
- Stochastic evolution of four species in cyclic competition
- Extinction in four species cyclic competition
- Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
- Synchronization and extinction in cyclic games with mixed strategies
- Three is much more than two in coarsening dynamics of cyclic competitions