The threshold of coexistence and critical behaviour of a predator–prey cellular automaton
Journal of Physics A: Mathematical and Theoretical, 40 (5):
887+ (Feb 2, 2007)DOI: 10.1088/1751-8113/40/5/002
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 mean-field approximations and numerical simulations we obtain the phase boundaries (thresholds) related to the transition between an active state, where prey and predators present a stable coexistence, and a prey absorbing state. The numerical 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.