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

TL;DR

This paper investigates a probabilistic cellular automaton modeling predator-prey coexistence and epidemic spreading, identifying phase transitions and critical behavior, including universality classes and crossover phenomena.

Contribution

It introduces a cellular automaton model capturing both predator-prey dynamics and epidemic spreading, analyzing critical thresholds and universality class transitions.

Findings

Transition belongs to directed percolation universality class

Identifies phase boundary between active coexistence and prey absorbing state

Observes crossover from directed percolation to dynamic percolation in epidemic model

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.