Collective Behavior: Macroscopic versus Kinetic Descriptions

Bifurcation dynamics in nonlocal hyperbolic models for self-organised aggregations

Raluca Eftimie

Dundee University

Nonlocal hyperbolic models that are used to describe self-organised aggregations (i.e., aggregations that form in the absence of any leader) can display a wide variety of spatial and spatio-temporal patterns: from classical stationary and rotating waves, to more exotic zigzags, ripples and modulated rotating waves. Here we investigate the codimension-1 and codimension-2 bifurcations that give rise to some of these patterns, and discuss the mechanisms behind the transitions between the patterns.