Oscillatory behaviour in a lattice prey-predator system

TL;DR

This study uses Monte Carlo simulations to demonstrate that a three-dimensional lattice prey-predator model exhibits persistent, stochastic resonance-induced oscillations, unlike lower-dimensional models, highlighting a novel microscopic stochastic dynamic phenomenon.

Contribution

The paper introduces the first microscopic stochastic prey-predator model showing intrinsic oscillations without external forcing, emphasizing the role of dimensionality and stochastic resonance.

Findings

Coherent oscillations occur in 3D but not in lower dimensions.

Oscillation amplitude remains finite in the thermodynamic limit.

Stochastic resonance likely induces the observed oscillations.

Abstract

Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in lower-dimensional models. Finite-size analysis indicate that amplitude of these oscillations is finite even in the thermodynamic limit. In our opinion, this is the first example of a microscopic model with stochastic dynamics which exhibits oscillatory behaviour without any external driving force. We suggest that oscillations in our model are induced by some kind of stochastic resonance.