import numpy as np

import smpl
from smpl import plot

print(smpl.__version__)

1.4.1

def gompertz(n, a, b):
    return -a * n * np.log(b * n)


def solution_gompertz(t, a, b, c):
    return 1 / b * np.exp(np.exp(-t * a) * c)

Multi Plot

Different color

Separation of Variables:

\[\int \frac{1}{N \ln (bN)} dN = \ln(\ln(bN)) +c= -adt =-at\]

\[\implies N(t) = \frac{1}{b} \exp (c \exp (-t a))\]

for a in [1, 2]:
    for b in [1, 0.5]:
        plot.function(
            gompertz, a, b, xaxis="$N$", yaxis="$\\dot N$", xmin=0.1, xmax=3, init=False
        )

for a in [1, 2]:
    for b in [1, 1 / 8]:
        for c in [1, 2]:
            plot.function(
                solution_gompertz,
                a,
                b,
                c,
                xaxis="$t$",
                yaxis="$N$",
                xmin=0.1,
                xmax=3,
                init=False,
                lpos=-1,
            )

Same color

for a in [1, 2]:
    for b in [1, 0.5]:
        plot.function(
            gompertz,
            a,
            b,
            xaxis="$N$",
            yaxis="$\\dot N$",
            xmin=0.1,
            xmax=3,
            init=False,
            next_color=a == b,
        )