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,) – (shape=(2, )) – Vector-valued RandomVariable that describes the belief over the initial value. Usually it is a Constant (noise-free) or Normal (noisy) Random Variable with \(2\)-dimensional mean vector and \(2 \times 2\)-dimensional covariance matrix. To replicate “classical” initial values use the Constant 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.

Return type