Global bifurcations in FitzHugh-Nagumo model

The FitzHugh-Nagumo (F-N) system [1] modelling the electrical potential in the nodal system of the heart is shown to have a rich dynamics. The results are synthesized in the global bifurcation diagram providing an overall view of all possible qualitatively distinct responses of the model for all values of the parameters. Since the curves of global bifurcation values emerge at points of curves consisting of local bifurcation values, the global bifurcations are presented in the context of the global bifurcation diagram. Thus, codimension one bifurcations of Hopf, homoclinic, saddle-node, breaking saddle connections, nonhyperbolic limit cycle and breaking the connection between a saddle and a saddle-node types are obtained. A large number of codimension two bifurcations are discussed here, such as Bogdanov-Takens, Bautin, double homoclinic, double breaking saddle connections bifurcations. Some of the bifurcation boundaries are obtained analytically, other are obtained numerically, using the software MATHEMATICA and our own code DIECBI [2].