Abstract or Additional Information
ABSTRACT: The FitzHugh-Nagumo system is a simple model for the propagation of action potentials along an axon; it is also a paradigm model for singular perturbation theory that has been used in the past to illuminate and explain dynamical structures found in other spatially extended systems. In this talk, I will give an overview of recent results on the existence and stability of fast travelling pulses with spatially oscillatory tails in the FitzHugh-Nagumo system. I will also discuss parametric transitions from single to double pulses that these waves exhibit when continuing them in systems parameters: similar dynamic transitions have been observed numerically in many other models, where they are often referred to as backring. The focus of this talk will be on the geometrical features that create pulses and their transitions and less on the proofs, which are based on a combination of Lins method and geometric singular perturbation theory. These results are joint works with Paul Carter and Bjrn de Rijk.
HOST: Jon Rubin