lotkavolterra

probnum.diffeq.lotkavolterra(timespan, initrv, params=0.5, 0.05, 0.5, 0.05)

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 \(f\).

Parameters

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

• initrv (RandomVariable,) – (shape=(2, )) – Vector-valued RandomVariable that describes the belief over the initial value. Usually it is a Constant (noise-free) or Normal (noisy) Random Variable with \(2\)-dimensional mean vector and \(2 \times 2\)-dimensional covariance matrix. To replicate “classical” initial values use the Constant distribution.

• params ((float, float, float, float), optional) – Parameters \((a, b, c, d)\) for the logistic IVP. Default is \((a, b, c, d)=(0.5, 0.05, 0.5, 0.05)\).

Returns

IVP object describing the logistic IVP with the prescribed configuration.

Return type

IVP