Stochastic Lattice Gas Model for a Predator-Prey System

TL;DR

This paper introduces a stochastic lattice gas model for predator-prey dynamics, capturing oscillatory behaviors and synchronization phenomena, analyzed through mean-field approximation and simulations.

Contribution

It presents a novel stochastic lattice gas model that incorporates predator-prey interactions and analyzes its behavior with mean-field and simulation methods.

Findings

System exhibits local oscillations in population densities

Mean-field predicts synchronized collective oscillations

Model captures key features of predator-prey dynamics

Abstract

We propose a stochastic lattice gas model to describe the dynamics of two animal species population, one being a predator and the other a prey. This model comprehends the mechanisms of the Lotka-Volterra model. Our analysis was performed by using a dynamical mean-field approximation and computer simulations. Our results show that the system exhibits an oscillatory behavior of the population densities of prey and predators. For the sets of parameters used in our computer simulations, these oscillations occur at a local level. Mean-field results predict synchronized collective oscillations.