CRM-McGill Applied Math Seminar
Tuesday April 1, 3:35pm
McGill, Burnside Hall Room 1205

Title: Interactions of spiral waves with media imperfections : a dynamical
systems approach

Victor G. LeBlanc
Department of Mathematics and Statistics
University of Ottawa

Since the pioneering work of Barkley in the mid-90s, finite-dimensional 
dynamical systems have been used successfully to predict many of the 
dynamical features and bifurcations of spiral (re-entrant) waves in 
excitable media.  Typically, the systems in which these waves occur are 
modelled using reaction-diffusion partial differential equations (RDPDEs), 
and as such, represent dynamical systems on infinite-dimensional phase 
spaces.  The reduction to finite-dimensional dynamics is done via center 
manifold reductions onto manifolds whose geometry is determined by the 
Euclidean symmetry (translations and rotations) of the underlying RDPDE.

In media where inhomogeneities and/or anisotropy is present, the Euclidean 
symmetry of the RDPDE is broken, and this affects the dynamics on the 
center manifold equations. In this talk, I will present some work by 
myself, my colleagues and my students on this problem of broken symmetry. 
Using techniques from dynamical systems, one can prove the existence of 
hyperbolic attractors on these center manifolds whose physical 
interpretation are consistent with some experimentally observed states for 
spiral waves, for example, anchoring (pinning) on inhomogeneities, and 
phase-locking/drifting of meandering waves in anisotropic media.