Speaker
Description
Understanding the mechanisms underlying the self-organisation of mobile organisms is a central question in spatial ecology and population dynamics. In many biological systems, individuals - from cells to animals - sense their environment before moving, leading naturally to nonlocal movement responses. Empirical evidence increasingly supports the importance of such nonlocal interactions, and mathematical models incorporating them provide a richer and more realistic description of collective behaviour.
In this talk, I will present a class of nonlocal advection-diffusion equations modelling population movement driven by spatially extended species interactions. Combining analytical and numerical approaches, I will show how the interplay between sensing range, interaction strength, and diffusion gives rise to a wide spectrum of spatio-temporal dynamics, including aggregation, segregation, time-periodic behaviour, and chase-and-run phenomena. I will discuss the emergence of multistability and hysteresis, and describe bifurcation mechanisms organising transitions between different spatial patterns. Overall, the talk will illustrate how nonlocal movement processes lead to qualitatively new dynamical regimes and mathematical challenges in models of spatial population dynamics.
