Title: Chaotic Patterns in Chemotaxis
Speaker: Thomas Hillen, University of Alberta
Abstract: Chemotaxis describes the active orientation of moving individuals along chemical gradients. The Keller-Segel model for chemotaxis has become famous through the existence of finite-time blow up solutions.
In this talk we add logistic growth to the chemotaxis model. Instead of blow-up we obtain global solutions which show interesting spatio-temporal chaotic patterns. I will motivate this model and analyse the resulting patterns. We find positive Lyapunov exponents and a period doubling sequence, both indications of chaotic behavior. Furthermore, I will present a discrete dynamical system, which can, surprisingly, reproduce most of these patterns. (joint work with K.J. Painter and J. Zielinski).