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.