Bifurcation structure of rotating wave solutions of the Fitzhugh-Nagumo equations

The FitzHugh-Nagumo (FHN) equations are model equations for nerve cell behavior. They support traveling wave solutions which depend on certain parameters. In this paper, a two parameter study of rotating wave solutions (i.e. periodic wavetrains) are considered. These solutions arise from bifurcations of stationary equilibria. The local bifurcation equations are analyzed to determine bifurcation directions as functions of the parameters. In addition, dependence on parameters is computed by numerical continuation and properties of the rotating wave solutions are summarized in parameter space. Finally, some of the biological implications are discussed.