String networks with junctions in competition models

TL;DR

This paper investigates the formation and evolution of string networks with junctions in multi-species competition models, analyzing their scaling behavior through simulations and mean field theory.

Contribution

It provides specific examples of multi-species competition models that naturally develop string networks with junctions and studies their dynamics and scaling properties.

Findings

Networks reach scaling regimes with length proportional to t^{1/2}

Junctions do not significantly alter the networks' scaling behavior

Both stochastic and mean field simulations confirm the scaling laws

Abstract

In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high concentration of enemy species. We study the two- and three-dimensional evolution of such networks, both using stochastic network and mean field theory simulations. If the predation, reproduction and mobility probabilities do not vary in space and time, we find that the networks attain scaling regimes with a characteristic length roughly proportional to $t^{1/2}$, where $t$ is the physical time, thus showing that the presence of junctions, on its own, does not have a significant impact on their scaling properties.