FitzHugh–Nagumo model

The FitzHugh–Nagumo model (FHN), named after Richard FitzHugh (1922 – 2007) who suggested the system in 1961 and J. Nagumo et al. who created the equivalent circuit the following year, describes a prototype of an excitable system (e.g., a neuron).

The FHN Model is an example of a relaxation oscillator because, if the external stimulus ${\displaystyle I_{\text{ext}}}$ exceeds a certain threshold value, the system will exhibit a characteristic excursion in phase space, before the variables ${\displaystyle v}$ and ${\displaystyle w}$ relax back to their rest values.

This behaviour is typical for spike generations (a short, nonlinear elevation of membrane voltage ${\displaystyle v}$, diminished over time by a slower, linear recovery variable ${\displaystyle w}$) in a neuron after stimulation by an external input current.

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