Bifurcations and Canards in the FitzHugh–Nagumo System: A Tutorial of Fast–Slow Dynamics

In this paper, we study the FitzHugh–Nagumo [Formula: see text]-fast–slow system where the vector fields associated to the fast/slow equations come from the reduction of the Hodgkin–Huxley model for the nerve impulse. After deriving the dynamical properties of the singular and regular cases, we perform a bifurcation analysis and investigate how the parameters (of the affine slow equation) impact the dynamics of the system. The study of codimension-1 bifurcations and the numerical locus of canards concludes this case study. All theoretical results are numerically illustrated.