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
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