In this diploma thesis we will discuss the logistic differential equation, which is
useful when dealing with models of growth of populations of certain species, as well
as in many other areas, which will be presented through examples. We will start
with the exponential growth model and show its weakness due to disregarding the
limiting factors. This is how we will gradually come to the introduction of the
logistic differential equation, which takes into account the limiting factors. In the
last section we will introduce a logistic differential equation with a critical threshold,
which takes into account the minimum population size in order to spread successfully.
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