Spatial organization in cyclic Lotka-Volterra systems

Abstract

We study the evolution of a system of $N$ interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5 species, spatial inhomogeneities develop spontaneously in initially homogeneous systems. The arising spatial patterns form a mosaic of single-species domains with algebraically growing size, $\ell (t)\sim t^{\alpha }$, where $\alpha =3/4$ (1/2) and 1/3 for N=3 with sequential (parallel) dynamics and N=4, respectively. The domain distribution also exhibits a self-similar spatial structure which is characterized by an additional length scale, $\mathcal{L}(t)\sim t^{\beta }$, with $\beta =1$ and 2/3 for N=3 and 4, respectively. For $N\ge 5$, the system quickly reaches a frozen state with non interacting neighboring species. We investigate the time distribution of the number of mutations of a site using scaling arguments as well as an exact solution for N=3. Some possible extensions of the system are analyzed.

18 pages, 10 figures, revtex, also available from http://arnold.uchicago.edu/~ebn/

References in corpus (19)

• Theory of Phase Ordering Kinetics
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Exact Results for Kinetics of Catalytic Reactions
• Coarsening and persistence in the voter model
• Stochastic Lattice Gas Model for a Predator-Prey System
• Persistent spins in the linear diffusion approximation of phase ordering and zeros of stationary gaussian processes
• Phase Ordering Kinetics of One-Dimensional Non-Conserved Scalar Systems
• Kinetics of Heterogeneous Single-Species Annihilation
• Proportion of Unaffected Sites in a Reaction-Diffusion Process
• Ballistic Annihilation Kinetics: The Case of Discrete Velocity Distributions
• Exact Results for Diffusion-Limited Reactions with Synchronous Dynamics
• Exact Exponent $\lambda$ of the Autocorrelation Function for a Soluble Model of Coarsening
• Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas
• Domain Growth in a 1-D Driven Diffusive System
• On War: The Dynamics of Vicious Civilizations
• Unwinding Scaling Violations in Phase Ordering
• Annihilation of Charged Particles
• Kinetics of phase ordering with topological textures
• Scaling Violations with Textures in Two-Dimensional Phase-Ordering

Cited by in corpus (75)

• Evolutionary games on graphs
• Cyclic dominance in evolutionary games: A review
• Coexistence versus extinction in the stochastic cyclic Lotka-Volterra model
• Bifurcations and Patterns in Compromise Processes
• Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
• Phase Transitions and Spatio-Temporal Fluctuations in Stochastic Lattice Lotka-Volterra Models
• Stochastic population dynamics in spatially extended predator-prey systems
• Cyclical interactions with alliance-specific heterogeneous invasion rates
• Phase Separation and Coarsening in One-Dimensional Driven Diffusive Systems: Local Dynaimcs Leading to Long-Range Hamiltonians
• Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates
• Spatial evolutionary prisoner's dilemma game with three strategies and external constraints
• Chimera states in population dynamics: networks with fragmented and hierarchical connectivities
• Ultimate Fate of Constrained Voters
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Phase transition in a spatial Lotka-Volterra model
• Effects of competition on pattern formation in the rock-paper-scissors game
• Exact solutions in multidimensional gravity with antisymmetric forms
• Defensive alliances in spatial models of cyclical population interactions
• Persistence in Complex Systems
• Entropy production of cyclic population dynamics
• A three-state cyclic voter model extended with Potts energy
• Cyclic competition of four species: domains and interfaces
• Segregation process and phase transition in cyclic predator-prey models with even number of species
• Residence Time Distribution for a Class of Gaussian Markov Processes
• Mobility and asymmetry effects in one-dimensional rock-paper-scissors games
• 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
• Co-existence in the two-dimensional May-Leonard model with random rates
• 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
• Saddles, Arrows, and Spirals: Deterministic Trajectories in Cyclic Competition of Four Species
• Globally synchronized oscillations in complex cyclic games
• Ballistic Annihilation
• On the relationship between cyclic and hierarchical three-species predator-prey systems and the two-species Lotka-Volterra model
• Stochastic evolution of four species in cyclic competition
• Evolutionary ecology in-silico:evolving foodwebs, migrating population and speciation
• Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations
• Extinction in four species cyclic competition
• Three-state Potts model in combination with the rock-scissors-paper game
• Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
• Instability of defensive alliances in the predator-prey model on complex networks
• Dynamically generated hierarchies in games of competition
• Mutation mitigates finite-size effects in spatial evolutionary games
• Three-fold way to extinction in populations of cyclically competing species
• Coexistence in a One-Dimensional Cyclic Dominance Process
• Competition of alliances in a cyclically dominant eight-species population
• Anomalous coarsening and glassy dynamics
• Nonextensivity of the cyclic Lattice Lotka Volterra model
• Slow Coarsening in an Ising Chain with Competing Interactions
• Coevolutionary dynamics of a variant of the cyclic Lotka-Volterra model with three-agent interactions
• Synchronization and extinction in cyclic games with mixed strategies
• Spreading of families in cyclic predator-prey models
• Aging and its Distribution in Coarsening Processes
• Fraction of uninfected walkers in the one-dimensional Potts model
• Environment driven oscillation in an off-lattice May--Leonard model
• Competition of coarsening and shredding of clusters in a driven diffusive lattice gas
• Coarsening of a Class of Driven Striped Structures
• Deterministic Soluble Model of Coarsening
• Stabilizing spiral structures in the asymmetric May-Leonard model
• Period Stabilization in the Busse-Heikes Model of the Kuppers-Lortz Instability
• Fronts, Domain Growth and Dynamical Scaling in a d=1 non-Potential System
• Three is much more than two in coarsening dynamics of cyclic competitions
• Predator-Prey Behaviour in Self-Replicating Interstellar Probes
• Long-Range and Many-Body Effects in Coagulation Processes
• Evolutionary Dynamics for Persistent Cooperation in Structured Populations
• Deterministic extinction by mixing in cyclically competing species
• Entropy production in the cyclic lattice Lotka-Volterra model
• Perturbative Field-Theoretical Analysis of Three-Species Cyclic Predator-Prey Models
• Evolutionary ecology in-silico: Does mathematical modelling help in understanding the "generic" trends?
• Higher order mass aggregation terms in a nonlinear predator-prey model maintain limit cycle stability in Saturn's F ring
• Non-Markovian Rock-Paper-Scissors games
• Quantization of Nambu Brackets from Operator Formalism in Classical Mechanics
• Shadow Hamiltonians of structure-preserving integrators for Nambu mechanics
• Nambu Non-equilibrium Thermodynamics: Axiomatic Formulation and Foundation