Anisotropic probabilistic cellular automaton for a predator-prey system

Abstract

We consider a probabilistic cellular automaton to analyze the stochastic dynamics of a predator-prey system. The local rules are Markovian and are based in the Lotka-Volterra model. The individuals of each species reside on the sites of a lattice and interact with an unsymmetrical neighborhood. We look for the effect of the space anisotropy in the characterization of the oscillations of the species population densities. Our study of the probabilistic cellular automaton is based on simple and pair mean-field approximations and explicitly takes into account spatial anisotropy.

Reaction-diffusion stochastic lattice model for a predator-prey system

“…We analyze the model by means of two levels of mean-field approximation: the simple (SMF) and pair (PMF) approximation [39,52]. In the SMF, the probability of a cluster of sites is approximated by a product of one-site probabilities.…”

Dinâmica estocástica de populações biológicas

“…Autômatos celulares foram utilizados, por exemplo, para descrever uma parte do sistema imunológico em [46] e para investigar o sistema predadorpresa em [47][48][49][50]. Recentemente um autômato celular foi introduzido [51] para analisar o comportamento do sistema predador-presa em uma rede fractal.…”