fitzhughnagumo

probnum.problems.zoo.diffeq.fitzhughnagumo(t0=0.0, tmax=20.0, y0=None, params=(0.2, 0.2, 3.0, 1.0))[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 parameters \((a, b, c, d)\). Default is \((a, b)=(0.2, 0.2, 3.0)\). This implementation includes the Jacobian \(J_f\) of \(f\).

Parameters
  • t0 – Initial time.

  • tmax – Final time.

  • y0(shape=(2, )) – Initial value. Defaults to [1., -1.].

  • params – Parameters (a, b, c, d) of the FitzHugh-Nagumo model.

Returns

InitialValueProblem object describing the FitzHugh-Nagumo model with the prescribed configuration.

Return type

InitialValueProblem