Dinâmica de aplicações simples : proposta de abordagem para o ensino básico

Abstract

This research aim to design a teaching sequence to relate the study of discrete dynamical systems and the composition functions from the logistic analysis model of Verhulst, considering a population with a constant birth rate and a mortality rate directly proportional to that population. Preliminary concepts of discrete dynamical study are presented, such as the concepts of iterate and equilibrium points, repelling, attracting, periodic, among others, followed by the classical results. Some motivator problems that can help understanding the importance of discrete dynamical study are shown. It appears the dynamic in a de ned interval and the graphic behavior of the quadratic family, culminating in the implementation of previous results in the logistic model evolution. Finally, we present a proposed teaching sequence, whose aims is to verify, from a given situation-problem with de ned values named initial conditions, the nal evolution, where possible, of a population P known the initial population Po.