Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
arXiv:1403.4319 · doi:10.1088/1751-8113/47/16/165001
Abstract
In order to model real ecological systems one has to consider many species that interact in complex ways. However, most of the recent theoretical studies have been restricted to few species systems with rather trivial interactions. The few studies dealing with larger number of species and/or more complex interaction schemes are mostly restricted to numerical explorations. In this paper we determine, starting from the deterministic mean-field rate equations, for large classes of systems the space of coexistence fixed points at which biodiversity is maximal. For systems with a single coexistence fixed point we derive complex Ginzburg-Landau equations that allow to describe space-time pattern realized in two space dimensions. For selected cases we compare the theoretical predictions with the pattern observed in numerical simulations.
22 pages, 5 figures, accepted for publication in the Journal of Physics A
References in corpus (20)
- Evolutionary games on graphs
- Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
- Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
- Self-Organization of Mobile Populations in Cyclic Competition
- Noise and Correlations in a Spatial Population Model with Cyclic Competition
- Oscillatory Dynamics in Rock-Paper-Scissors Games with Mutations
- Zero-one survival behavior of cyclically competing species
- Instability of spatial patterns and its ambiguous impact on species diversity
- Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates
- Junctions and spiral patterns in Rock-Paper-Scissors type models
- Coexistence and Survival in Conservative Lotka-Volterra Networks
- Effects of competition on pattern formation in the rock-paper-scissors game
- Self-organizing patterns maintained by competing associations in a six-species predator-prey model
- Segregation process and phase transition in cyclic predator-prey models with even number of species
- Intransitivity and coexistence in four species cyclic games
- Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species
- Interplay between partnership formation and competition in generalized May-Leonard games
- Stochastic evolution of four species in cyclic competition
- Three-fold way to extinction in populations of cyclically competing species
- Coexistence in a One-Dimensional Cyclic Dominance Process
Cited by in corpus (10)
- Cyclic dominance in evolutionary games: A review
- Stochastic population dynamics in spatially extended predator-prey systems
- Characterization of spiraling patterns in spatial rock-paper-scissors games
- The Influence of Mobility Rate on Spiral Waves in Spatial Rock-Paper-Scissors Games
- The effect of habitats and fitness on species coexistence in systems with cyclic dominance
- Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
- Dynamically generated hierarchies in games of competition
- Synchronization and extinction in cyclic games with mixed strategies
- Rock-paper-scissors played within competing domains in predator-prey games
- Quantized vortex dynamics of the complex Ginzburg-Landau equation on torus