lotkavolterra¶
- 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 \(f\).
- Parameters
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 Lotka-Volterra IVP. Default is \((a, b, c, d)=(0.5, 0.05, 0.5, 0.05)\).
- Returns
IVP object describing the Lotka-Volterra IVP with the prescribed configuration.
- Return type