title: [Logistic law of growth and its implications].
abstract: The "morphological" (i.e. structural and quantitative) properties of VERHULST's "Logistic Law of Growth" in its versions as differential equations and as analytical functions will be discussed. It follows the attempts of generalizations of the logistic law of growth by parameterization or by changing its structure due to adding parameters. Such an additional parameter is the constant term paying regard to the level (in y-direction) on which the (growth) process may start. The second manner of introducing additional parameters is the substitution of the independent variable in its linear form by a polynomial of degree k. These generalizations will be called "generalized logistic (growth-) function". Its "morphology" will be discussed. Special points there are the use of this function as empirical expression for smoothing and quantitative description of courses of measured values (of growth variables), and the genesis of the function type as solution of a first order differential equation. "Philosophy of the generalized law of growth" means a detailed discussion of properties which could be interpreted as "time structure", and of the modelling relevancy of the differential equations resp. of the analytical function expressions which represent the versions of the generalized logistic law.
mesh_terms: D006801:Humans; D008433:Mathematics; D011158:Population Growth
vernacular_title: Das Logistische Wachstumsgesetz und seine Erweiterungen.