String networks in Z_N Lotka-Volterra competition models

TL;DR

This paper explores how string networks form in Z_N Lotka-Volterra competition models, revealing that species organize around empty regions, with dynamics resembling physical systems in condensed matter and cosmology.

Contribution

It introduces specific Z_N Lotka-Volterra models that produce string networks and analyzes their formation and dynamics through simulations.

Findings

String networks form in the models due to predator-prey interactions.

Coarsening of networks follows a scaling law similar to physical systems.

Configurations extend into three dimensions, creating complex structures.

Abstract

In this letter we give specific examples of Z_N Lotka-Volterra competition models leading to the formation of string networks. We show that, in order to promote coexistence, the species may arrange themselves around regions with a high number density of empty sites generated by predator-prey interactions between competing species. These configurations extend into the third dimension giving rise to string networks. We investigate the corresponding dynamics using both stochastic and mean field theory simulations, showing that the coarsening of these string networks follows a scaling law which is analogous to that found in other physical systems in condensed matter and cosmology.