Discrete dynamics

Abstract

Difference equations, recursive relations, discrete mathematics,… namely rules for building number sequences, have been on the stage for centuries, mainly to define approximating procedures, especially in connection with numerical methods. However, in more recent years, iterative procedures arose in the context of the modeling of natural phenomena, and the concept of a (time) discrete dynamical system has been developed for a parallel and alternative approach to the theory based on differential equations. In Chap. 3 we have in fact discussed several population models, embedded in the framework of a time discrete description, here we give an account of some basic fact and results that we have used in the analysis. Some of the basic references have been already quoted in Chap. 3: 2 and 5; a more introductory presentation including Ordinary Differential Equations and Discrete Dynamical Systems is in 4 while 1 gives extended applications to ecological studies. Finally, 3 provides the basic results of the qualitative theory, while elementary and less elementary bifurcations are discussed in 6 and 7.