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

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

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

Parameters

timespan ((float, float)) – Time span of IVP.
initrv (RandomVariable,) – RandomVariable that describes the belief over the initial value. Usually its distribution is Constant (noise-free) or Normal (noisy). 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