Anisotropic probabilistic cellular automaton for a predator-prey system

TL;DR

This paper models predator-prey interactions using an anisotropic probabilistic cellular automaton based on Lotka-Volterra rules, analyzing how spatial anisotropy influences population oscillations through mean-field approximations.

Contribution

It introduces a novel anisotropic probabilistic cellular automaton model for predator-prey dynamics incorporating spatial anisotropy effects.

Findings

Anisotropy significantly affects oscillation patterns.

Mean-field approximations effectively capture spatial effects.

Model provides insights into spatially structured ecological systems.

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.