Solitonic description of interface profiles in competition models

TL;DR

This paper introduces a solitonic theoretical framework to describe and analyze the interface profiles in symmetric competition models, validated through numerical simulations in 2D and 3D.

Contribution

It presents a novel solitonic formalism for static interface profiles in symmetric competition models, linking topological properties to network dynamics.

Findings

Theoretical functions accurately describe interface properties.

Numerical simulations confirm the model's fit.

Interfaces exhibit solitonic characteristics.

Abstract

We consider systems with two competing species whose actions are completely symmetric, with same mobility, reproduction and competition rates. Numerical implementations of the model in two and three-dimensional space show that regions of single species are formed by spontaneous symmetry breaking. We propose a theoretical formalism for describing the static profile of the interfaces of empty spaces separating domains with different species. We compute the topological properties of the interfaces and show that these theoretical functions are useful to the understanding of the dynamics of the network. Finally, we compare the theoretical functions with results from the numerical implementation of the mean field equations and verify that our model fits well the properties of interfaces.