Cyclic competition of four species: domains and interfaces

TL;DR

This paper investigates how four-species cyclic interactions influence domain growth and interface fluctuations in one- and two-dimensional lattice systems, revealing mobility-dependent growth in chains and universal regimes in two dimensions.

Contribution

It introduces a numerical study of domain and interface dynamics in cyclic four-species systems, highlighting the effects of particle mobility and neutral exchanges.

Findings

Higher mobility increases domain growth exponent in chains.

In two dimensions, neutral exchanges lead to universal growth and fluctuation regimes.

Interface fluctuations become independent of predation and exchange rates in 2D.

Abstract

We study numerically domain growth and interface fluctuations in one- and two-dimensional lattice systems composed of four species that interact in a cyclic way. Particle mobility is implemented through exchanges of particles located on neighboring lattice sites. For the chain we find that domain growth strongly depends on the mobility, with a higher mobility yielding a larger domain growth exponent. In two space dimensions, when also exchanges between mutually neutral particles are possible, both domain growth and interface fluctuations display universal regimes that are independent of the predation and exchange rates.