# logistic¶

probnum.diffeq.logistic(timespan, initrv, params=3.0, 1.0)[source]

Initial value problem (IVP) based on the logistic ODE.

The logistic ODE is defined through

$f(t, y) = a y \left( 1 - \frac{y}{b} \right)$

for some parameters $$(a, b)$$. Default is $$(a, b)=(3.0, 1.0)$$. This implementation includes the Jacobian $$J_f$$ of $$f$$ as well as a closed form solution given by

$f(t) = \frac{b y_0 \exp(a t)}{b + y_0 \left[ \exp(at) - 1 \right]}$

where $$y_0= y(t_0)$$ is the initial value.

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

• initrv (RandomVariable,) – (shape=()) – Scalar-valued RandomVariable that describes the belief over the initial value. Usually it is a Constant (noise-free or Normal (no Random Variable isy) with scalar mean and scalar variance. To replicate “classical” initial values use the Constant distribution.

• params ((float, float), optional) – Parameters $$(a, b)$$ for the logistic IVP. Default is $$(a, b) = (3.0, 1.0)$$.

Returns

IVP object describing the logistic IVP with the prescribed configuration.

Return type

IVP