Abstract

In this talk, we study a model for territorial development. We begin with a lattice model, where agents from two species are moving on a lattice and each agent puts down species-specific markings as it moves. The agents then try to avoid the other species’ markings. We find a phase transition where in some parameter regimes, the species segregate into two distinct territories, while in other regimes they remain mixed. We take a continuum limit to derive a set of coupled convection-diffusion equations from the lattice model, and we study the phase transition from this macroscopic perspective. We then discuss recent extensions of this work.