probnum.diffeq.lotkavolterra(timespan, initrv, 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 some 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 \(f\).

  • 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 \((a, b, c, d)=(0.5, 0.05, 0.5, 0.05)\).

IVP object describing the logistic IVP with the prescribed configuration.

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