So for instance with respect to the (continuous form of the) Logistic Equation
which gives a more realistic description of population dynamics. Here p stands for population size, m is the population growth factor, and n is the inhibition factor.
dp / dt is the rate of change of p in time.
The solution of this non-linear equation reads :
(where e is a mathematical constant). This turns out to be an S-shaped curve which shows the course of p in time (starting at t+k) (See D'Arcy THOMPSON, 1942, On Growth and Form, p.147).
This S-shaped curve cannot directly be read off from the (non-linear) equation
dp / dt = mp - np2 .