# lorenz¶

probnum.problems.zoo.diffeq.lorenz(t0=0.0, tmax=20.0, y0=None, 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
• t0 – Initial time. Default is 0.0

• tmax – Final time. Default is 20.0

• y0(shape=(3, )) – Initial value. Default is [0., 1., 1.05].

• params – Parameter of the Lotka-Volterra model. Default is (0.2, 0.2, 3.0).

Returns

InitialValueProblem object describing the Lorenz system with the prescribed configuration.

Return type

InitialValueProblem