probnum.problems.zoo.diffeq.lotkavolterra(t0=0.0, tmax=20.0, y0=None, params=(0.5, 0.05, 0.5, 0.05))[source]

Initial value problem (IVP) based on the Lotka-Volterra model.

The Lotka-Volterra (LV) model is defined through

\[\begin{split}f(t, y) = \begin{pmatrix} a y_1 - by_1y_2 \\ -c y_2 + d y_1 y_2 \end{pmatrix}\end{split}\]

for parameters \((a, b, c, d)\). Default is \((a, b)=(0.5, 0.05, 0.5, 0.05)\). This implementation includes the Jacobian \(J_f\) of \(f\).

  • t0 – Initial time.

  • tmax – Final time.

  • y0(shape=(2, )) – Initial value. Defaults to [20., 20.].

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


InitialValueProblem object describing the Lotka-Volterra system with the prescribed configuration.

Return type