Fig. 1

Canards in the FHN system (Equations 1a-1b) at $a=-1.3$, $b=-0.3$, $\epsilon =0.05$. (a) Bifurcation diagram of the full system showing fixed points (black curve) and periodic orbits (two red curves, indicating maximal and minimal values of V over the orbit). Solid/dashed curves indicate stable/unstable solutions. (b)-(f) The $(V,w)$ phase plane, including trajectories (red curves) of the full system at several fixed values of I. Arrows indicate the direction of flow. Each phase plane also includes the cubic V-nullcline $w=V-V^3/3-I$, labeled $\dot{V}=0$ and plotted as a solid/dashed curve when it corresponds to a branch of attracting/repelling fixed points of the fast system. The w-nullcline $w=(V-a)/b$, labeled $\dot{w}=0$, is included in (b) but excluded from the other phase space plots for clarity.