Lattice Symmetry Breaking Perturbation for Spiral Waves

Abstract

Spiral waves occur in several natural phenomena, including reaction fronts in two-dimension excitable media. In this thesis we attempt to characterize the motion of the spiral tip of a rigidly rotating wave and a linearly travelling wave in the context of a lattice perturbation. This system can be reduced to its center manifold, which allows us to describe the system as ordinary differential equations. This in turn means dynamical systems methods are appropriate to describe the motion of the tip. It is in such a context that we work on spiral waves. We study perturbed rotating waves and travelling waves using standard techniques from dynamical systems theory.