Note 31

So for instance with respect to the (continuous form of the) Logistic Equation

dp / dt = mp - np2

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 .

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