MPI-DS Colloquium: Understanding self-organisation in nature

Patterns and Bifurcations in Nonlocal Advection-Diffusion Models Understanding the mechanisms behind the spatial distribution of organisms is a central issue in both ecology and cell biology. In nature individuals, whether cells or animals, inspect their environment before moving. This process is typically nonlocal, meaning that individuals gather information from a part of their environment rather than just their immediate location. Empirical research increasingly highlights nonlocality as a key aspect of movement, while mathematical models incorporating nonlocal interactions have gained attention for their ability to describe how interactions shape movement and spatial distribution.
In this talk, I will present the study of a class of advection-diffusion equations that model population movement driven by nonlocal interactions between species. Using a combination of analytical and numerical tools, I will show that these models support a wide range of spatio-temporal solutions, modelling segregation, aggregation, time-periodic behaviour, and chase-and-run dynamics. I will discuss various methods for analysing the bifurcation and pattern formation properties of this class of models, which are essential for under-standing many aggregation phenomena observed in nature.