# fitzhughnagumo¶

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 $$f$$.

Parameters: 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. IVP