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

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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