Logistic curve of N-th order and compound growth modeling

A notion of generalized logistic curve (so-called logistic curve of N-th order) is introduced. The important property of this curve is existence of several points of inflection. This makes it applicable for analysis and forecasting many economical indices. For estimation of parameters of logistic curve of N-th order a method is proposed which is analogue of the Rhode's method firstly proposed for simple logistic curve. It is shown that logistic curve of N-th order is solution to a system of non-linear differential equations which may describe the compound growth in multi-level production system or dynamic behavior of trophic chain of a biological populations.