Systèmes dynamiques
Codimension two bifurcations in animal aggregation models with symmetry
Buono, Pietro-Luciano
University of Ontario Institute of Technology

Pattern formation in self-organised biological aggregation is a phenomenon that has been studied intensively over the past twenty years. I will present a class of models of animal aggregation in the form of two first-order hyperbolic partial differential equations on a one-dimensional domain with periodic boundary conditions, describing the motion of left and right moving individuals. The nonlinear terms appear using nonlocal social interaction terms for attraction, repulsion and alignment. This class of models has been introduced in the Ph.D thesis of R. Eftimie. In this talk, I will show that the equations are O(2) equivariant where the group O(2) is generated by space-translations and a reflection which interchanges left-moving individuals with right-moving individuals across the middle of the interval. I will show the existence of codimension two steady-state/steady-state, steady-state/Hopf and Hopf/Hopf bifurcation points with O(2) symmetry. Using the existing symmetry-breaking bifurcation theory, one can study the neighborhood of those bifurcation points and classify the patterns obtained. This is joint work with R. Eftimie (U. Dundee, Scotland).

Mardi, 18 juin, 11h00
Salle Des Plaines A