Symmetry-breaking bifurcations in one-dimensional excitable media

A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear stability analysis is used to determine bifurcations of these solutions. It is shown that the sequence of symmetry-breaking bifurcations which lead from the homogeneous excitable state to stable traveling waves can be understood in terms of an O(2)-symmetric normal form.