**David Stearns, Department of Applied Mathematics, University of Colorado Boulder**

*Dynamics and Analysis of Territorial Animals*

The ways animals form territories, interact with members of their own social group, and interact with members of other intraspecies social groups play a vital role in the maintenance of an ecosystem and in the evolution of these species. Understanding these territories is also key to evaluating the human impact on these ecosystems through both direct interaction and the effects of climate change. This project focuses on two possible mathematical models for how these territories form and change; they are a discrete interacting particle model, where individuals attract and repel each other based on their identity and the environment, and a continuous advection-diffusion partial differential equation model, in which the groups are modeled as density functions which attract and repel each other. In particular, the threshold for when the discrete model becomes a good approximation to the advection-diffusion model is of particular importance.