  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.
