Oscillations and dynamics in a two-dimensional prey-predator system

TL;DR

This study uses Monte Carlo simulations to analyze two-dimensional prey-predator systems, finding that temporal oscillations of species densities vanish in large systems and exploring critical behavior near phase transitions.

Contribution

The paper demonstrates that local dynamics do not sustain oscillations in large two-dimensional prey-predator models and investigates the critical behavior using dynamical Monte Carlo methods.

Findings

Temporal oscillations vanish in the thermodynamic limit.

The model exhibits a phase transition between active and absorbing states.

Dynamical Monte Carlo reveals critical behavior near the transition.

Abstract

Using Monte Carlo simulations we study two-dimensional prey-predator systems. Measuring the variance of densities of prey and predators on the triangular lattice and on the lattice with eight neighbours, we conclude that temporal oscillations of these densities vanish in the thermodynamic limit. This result suggests that such oscillations do not exist in two-dimensional models, at least when driven by local dynamics. Depending on the control parameter, the model could be either in an active or in an absorbing phase, which are separated by the critical point. The critical behaviour of this model is studied using the dynamical Monte Carlo method. This model has two dynamically nonsymmetric absorbing states. In principle both absorbing states can be used for the analysis of the critical point. However, dynamical simulations which start from the unstable absorbing state suffer from metastable-like effects, which sometimes renders the method inefficient.