# 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
• 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