lorenz

probnum.diffeq.lorenz(timespan, initrv, params=(10.0, 28.0, 2.6666666666666665))[source]

Initial value problem (IVP) based on the Lorenz system.

The Lorenz system is defined through

\[\begin{split}f(t, y) = \begin{pmatrix} a(y_2 - y_1) \\ y_1(b-y_3) - y_2 \\ y_1y_2 - cy_3 \end{pmatrix}\end{split}\]

for some parameters \((a, b, c)\). Default is \((a, b, c)=(10, 28, 2.667)\). This implementation includes the Jacobian \(J_f\) of \(f\).

Parameters
  • timespan ((float, float)) – Time span of IVP.

  • initrv (RandomVariable,) – (shape=(3, )) – Vector-valued RandomVariable that describes the belief over the initial value. Usually it is a Constant (noise-free) or Normal (noisy) Random Variable with \(3\)-dimensional mean vector and \(3 \times 3\)-dimensional covariance matrix. To replicate “classical” initial values use the Constant distribution.

  • params ((float, float, float, float), optional) – Parameters \((a, b, c)\) for the Lorenz system. Default is \((a, b, c)=(10, 28, 2.667)\).

Returns

IVP object describing the Lorenz system IVP with the prescribed configuration.

Return type

IVP