A nonlinear discrete model: the logistic map

Abstract In this section we want to continue our discussion of the growth model presented in Chapter 20, the logistic law, illustrating the dynamics of the version in discrete time (20.4). We are particularly interested in showing how a simple nonlinear growth model such as (20.4), that determines the logistic growth of a population, can in some cases generate chaos. In Chapter 22 we will be illustrating various examples produced by means of numerical simulations, as well as some applications of the logistic map in regional sciences. Readers interested in a complete description of the properties of the dynamics of the logistics map can find detailed and in-depth discussions of the mathematical aspects, which in this text are only briefly mentioned, in two fundamental articles. These are works that have reproposed the logistic map to scholars in recent decades, more than a century after Verhulst introduced it: the work of Robert May (1976), the first, in recent years to examine the properties of the map, and that of Mitchell Feigenbaum (1978), whose content is more technical, in which specific aspects are looked at in more depth and generalized.