Fig. 7.

Phase plane analysis of Type II–Type I–Type II* transitions in a 2D reduction of the Connor–Stevens model. (A) FI curves in a 2D reduced Connor–Stevens model (see Methods) for three different values of ${\overline{g}}_A$ corresponding to (Left) Type II, (Middle) Type I, and (Right) Type II*. Bifurcation types are indicated at the respective values of the applied current (Hopf, Andronov–Hopf; SN, Saddle Node; FLC, Fold Limit Cycle). Stars indicate the value of the applied current at which each phase plane is plotted. (B) Phase planes computed at spiking threshold for each of the three ${\overline{g}}_A$ cases. The specific bifurcation induced by applied current, I_app, is indicated on each plot (I_Hopf, Andronov–Hopf bifurcation; I_SNIC, Saddle Node on Invariant Circle; I_SN, Saddle Node). Open circles correspond to unstable fixed points, black filled circles correspond to stable fixed points, and half-filled circles correspond to saddle node points. V nullclines are shown in blue, and w nullclines are shown in green. (Insets) Phase plane detail during repetitive spiking; red dotted arrows indicate membrane potential trajectories.