Threshold of coexistence and critical behavior of a predator-prey cellular automaton

Abstract

We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out time-dependent simulations we obtain the dynamic critical exponents and the phase boundaries (thresholds) related to the transition between an activestate, where prey and predators present a stable coexistence, and a prey absorbing state. The estimates for the critical exponents show that the transition belongs to the directed percolation universality class. In the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class. Patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed.

10 pages, 11 figures

References in corpus (3)

• Fluctuations and Correlations in Lattice Models for Predator-Prey Interaction
• Mean Field Approximation to a Spatial Host-Pathogen Model
• Self-organized patterns of coexistence out of a predator-prey cellular automaton

Cited by in corpus (8)

• On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
• Stochastic lattice gas model describing the dynamics of an epidemic
• Finite-size scaling of the stochastic susceptible-infected-recovered model
• Stable oscillations of a predator-prey probabilistic cellular automaton: a mean-field approach
• Critical properties of the susceptible-exposed-infected model on a square lattice
• Active-to-absorbing-state phase transition in an evolving population with mutation
• Absorbing Phase Transition in a Four State Predator Prey Model in One Dimension
• Crossover from dynamical percolation class to directed percolation class on a two dimensional lattice