[STAT/AP] Alethea Barbaro: A model for territorial development: from particles to continuum

08 January 2024 15:45 till 16:45 - Location: Lecture Hall Chip | Add to my calendar

Many species demonstrate territoriality, with individuals or groups marking their territories either chemically or visually.  In this talk, we will present an agent-based lattice model for territorial development. In this model, there are several groups, and agents from each group put down that group’s territorial markings as they move on the lattice. Agents move away from areas with territorial markings which do not belong to their own group. We will show that this model undergoes a phase transition between well-mixed collective dynamics and distinct territories as parameters are varied.  We will then discuss the derivation of a system of coupled convection-diffusion equations from this model. This system exhibits cross-diffusion due to the avoidance of other groups’ markings. We will pinpoint the critical value for the phase transition using linear stability analysis and discuss further analytical and numerical work stemming from this model.