Spatial Rock-Paper-Scissors Models with Inhomogeneous Reaction Rates

TL;DR

This study investigates how spatial variability and site restrictions affect the dynamics of a stochastic three-species rock-paper-scissors model, finding that these factors have minimal impact on long-term coexistence and system behavior.

Contribution

The paper demonstrates that in three-species cyclic models, quenched disorder and site restrictions have little effect on dynamics, highlighting the robustness of spatial rock-paper-scissors systems.

Findings

Quenched disorder in reaction rates has minimal impact on long-term dynamics.

Site restrictions only slightly influence the system's behavior.

Stochastic fluctuations and spatial correlations are less significant than expected.

Abstract

We study several variants of the stochastic four-state rock-paper-scissors game or, equivalently, cyclic three-species predator-prey models with conserved total particle density, by means of Monte Carlo simulations on one- and two-dimensional lattices. Specifically, we investigate the influence of spatial variability of the reaction rates and site occupancy restrictions on the transient oscillations of the species densities and on spatial correlation functions in the quasi-stationary coexistence state. For small systems, we also numerically determine the dependence of typical extinction times on the number of lattice sites. In stark contrast with two-species stochastic Lotka-Volterra systems, we find that for our three-species models with cyclic competition quenched disorder in the reaction rates has very little effect on the dynamics and the long-time properties of the coexistence state. Similarly, we observe that site restriction only has a minor influence on the system's dynamical properties. Our results therefore demonstrate that the features of the spatial rock-paper-scissors system are remarkably robust with respect to model variations, and stochastic fluctuations as well as spatial correlations play a comparatively minor role.