Solitonic description of interface profiles in competition models

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.