# Canard explosion in the FitzHugh-Nagumo model

### Bifurcation and Continuation

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This animation illustrates the phenomenon of canard explosion in the FitzHugh-Nagumo model. This model mimics the evolution of the membrane potential V(t) of a neuron depending on an applied current I. The branch of limit cycles born at a Hopf bifurcation HB (top left panel) shows a sharp almost-vertical" segment. In the associated time series (top right panel) this corresponds to a brutal transition from small-amplitude sub-threshold oscillations to spiking oscillation, that is, action potentials. In the parameter/variable space (IVw) (bottom panel), one can recognize the classical duck-shape periodic orbits called canards. They organize this rapid transition from stable stationary solutions before the Hopf point (solid line) to large-amplitude (relaxation-type) limit cycles.

 Author Institutional Affiliation The University of Bristol Author Email [email protected] Author Postal Mail Dept of Eng. Maths University Walk Bristol BS8 1TR UK Keywords slow-fast systems, canard phenomenon