Mobility and asymmetry effects in one-dimensional rock-paper-scissors games

Abstract

As the behavior of a system composed of cyclically competing species is strongly influenced by the presence of fluctuations, it is of interest to study cyclic dominance in low dimensions where these effects are the most prominent. We here discuss rock-paper-scissors games on a one-dimensional lattice where the interaction rates and the mobility can be species dependent. Allowing only single site occupation, we realize mobility by exchanging individuals of different species. When the interaction and swapping rates are symmetric, a strongly enhanced swapping rate yields an increased mixing of the species, leading to a mean-field like coexistence even in one-dimensional systems. This coexistence is transient when the rates are asymmetric, and eventually only one species will survive. Interestingly, in our spatial games the dominating species can differ from the species that would dominate in the corresponding nonspatial model. We identify different regimes in the parameter space and construct the corresponding dynamical phase diagram.

6 pages, 5 figures, to appear in Physical Review E

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• Cyclic competition of four species: domains and interfaces
• Intransitivity and coexistence in four species cyclic games
• Interplay between partnership formation and competition in generalized May-Leonard games
• Uneven rock-paper-scissors models: patterns and coexistence
• Global attractors and extinction dynamics of cyclically competing species
• Cyclic competition of four species: mean field theory and stochastic evolution
• Saddles, Arrows, and Spirals: Deterministic Trajectories in Cyclic Competition of Four Species
• A theoretical approach to understand spatial organization in complex ecologies
• The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games
• On the relationship between cyclic and hierarchical three-species predator-prey systems and the two-species Lotka-Volterra model
• Hamming distance and mobility behavior in generalized rock-paper-scissors models
• 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
• Three-fold way to extinction in populations of cyclically competing species
• Basin entropy behavior in a cyclic model of the rock-paper-scissors type
• Mortality makes coexistence vulnerable in evolutionary game of rock-paper-scissors
• Survival behavior in the cyclic Lotka-Volterra model with a randomly switching reaction rate
• Synchronization and extinction in cyclic games with mixed strategies
• Three is much more than two in coarsening dynamics of cyclic competitions
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations
• Emergence of first-order and second-order phase transitions in a cyclic ecosystem exposed to environmental impact