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.