Georg Gottwald School of Mathematics and Statistics, University of Sydney A normal form for excitable media Wednesday 26th April 14:05-14:55pm, Carslaw Building Room 373. We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behaviour of single pulses in a periodic domain and also the richer behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement. We then study the Hopf bifurcation by means of center manifold theory. We find the Hopf bifurcation to be subcritical for all parameter values. This has interesting consequences for cardiac dynamics and so called alternans, which have so far been believed to be stable oscillations. We confirm our theoretical result by numerical simulations.