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.
%0 Journal Article
%1 Arashiro2007Threshold
%A Arashiro, Everaldo
%A Tomé, Tânia
%D 2007
%J Journal of Physics A: Mathematical and Theoretical
%K cellular\_automata, sync-updates epidemic-models lattice-models
%N 5
%P 887+
%R 10.1088/1751-8113/40/5/002
%T The threshold of coexistence and critical behaviour of a predator–prey cellular automaton
%U http://dx.doi.org/10.1088/1751-8113/40/5/002
%V 40
%X 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.
@article{Arashiro2007Threshold,
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.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Arashiro, Everaldo and Tom\'{e}, T\^{a}nia},
biburl = {https://www.bibsonomy.org/bibtex/24a2973960f8fc91903a81c9347d91c05/nonancourt},
citeulike-article-id = {12586058},
citeulike-linkout-0 = {http://dx.doi.org/10.1088/1751-8113/40/5/002},
citeulike-linkout-1 = {http://iopscience.iop.org/1751-8113/40/5/002},
day = 02,
doi = {10.1088/1751-8113/40/5/002},
interhash = {46c8b87688c2b777ebe7bb01c1698e6e},
intrahash = {4a2973960f8fc91903a81c9347d91c05},
issn = {1751-8113},
journal = {Journal of Physics A: Mathematical and Theoretical},
keywords = {cellular\_automata, sync-updates epidemic-models lattice-models},
month = feb,
number = 5,
pages = {887+},
posted-at = {2013-08-19 20:02:11},
priority = {2},
timestamp = {2019-08-01T15:36:09.000+0200},
title = {{The threshold of coexistence and critical behaviour of a predator–prey cellular automaton}},
url = {http://dx.doi.org/10.1088/1751-8113/40/5/002},
volume = 40,
year = 2007
}