The Mathematics of Growth with Saturation A Model Analysis

In this paper mathematical extensions
and generalizations of the Pearl-Reed
model for'growth with saturation are
discussed. The derived differential
eqUation are of Bernoulli and Riccati
type that owing to their special forms
could be explicitely integrated resulting
in closed form solutions. The asymptotic
bahaviour of the system in each case
is briefly examined and the results are
compared with each other. The mathematical
models thus obtained have applications
in such diverse fields as analysis
of energy resources, population
etc., which are described in the paper
as different examples. These applications
are of importance in Energy,
Economic, and other planning activities,
for Iran.