probnum.diffeq.fitzhughnagumo(timespan, initrv, params=(0.0, 0.08, 0.07, 1.25))[source]

Initial value problem (IVP) based on the FitzHugh-Nagumo model.

The FitzHugh-Nagumo (FHN) model is defined through

\[\begin{split}f(t, y) = \begin{pmatrix} y_1 - \frac{1}{3}y_1^3 - y_2 + a \\ \frac{1}{d} (y_1 + b - c y_2) \end{pmatrix}\end{split}\]

for some parameters \((a, b, c, d)\). Default is \((a, b)=(0.0, 0.08, 0.07, 1.25)\). This implementation includes the Jacobian \(J_f\) of \(f\).

  • timespan ((float, float)) – Time span of IVP.
  • initrv (RandomVariable,) – RandomVariable that describes the belief over the initial value. Usually its distribution is Dirac (noise-free) or Normal (noisy). To replicate “classical” initial values use the Dirac distribution.
  • params ((float, float, float, float), optional) – Parameters \((a, b, c, d)\) for the logistic IVP. Default is \((a, b, c, d)=(0.0, 0.08, 0.07, 1.25)\).

IVP object describing the logistic IVP with the prescribed configuration.

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