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Fig. 6.5 Solutions of the
logistic equation depending
on the population
reproducibility
the population disappears. By direct calculations it is easy to show that if the value
is between 1 and 3, the solution actually tends to some asymptotic value (Fig.
6.5
).
But in the interval 3
<ʱ<
3.45 the solution oscillates between two values, in the
interval 3.45
3.54 between four values, and then falls into the region of chaos,
when predicting the value of the solution is not possible.
Physically, the behavior of the solution can be qualitatively explained by taking
into account that the processes of reproduction of population and its degradation
must occur with some time lag.
Yet we should note that the logistic equation used for solving various problems
is an ideal model that does not always correspond to actual processes of evolution of
a complex system.
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