Two-parameter bifurcation analysis of firing activities in the Chay neuronal model

The parameter regions for different firing patterns in the Chay neuronal model are presented and classified by using both two-parameter bifurcations and fast-slow dynamics analysis. Firing arises via a supercritical Hopf bifurcation of the whole system and disappears via a fold limit cycle bifurcation, respectively. Complex firing phenomena, including "fold/fold" bursting, "fold/Hopf" bursting, "fold/homoclinic" bursting, chaotic bursting, as well as chaotic and periodic spiking, are found in the firing area. The transitions of bursting activities can be determined by the codimension-1 and codimension-2 bifurcations of the fast subsystems in the two-parameter plane. It is seen that the dynamical analysis of different firing activities of neurons is closely related to the global bifurcation of the whole system as well as the two-parameter bifurcations of the fast subsystems.