Sistemas dinâmicos discretos: uma introdução às Equações de Diferenças e um breve estudo de modelos populacionais

Abstract

This work presents an introduction to Discrete Dynamic Systems, an area that has great prominence in modeling phenomena and predicting future events based on past events. In the study of these systems, the difference equations have great prominence, being these a discrete version of the differential equations. Thus, we will present some concepts that help in solving these equations, such as the concepts of homogeneous and non-homogeneous linear difference equations, similarly, we perform the same process for autonomous and nonautonomous linear systems, focusing on two-dimensional, that is, involving two equations. When we study phenomena that evolve over time, it is necessary to understand the behavior of the model in question. For this, we will study some concepts of stability and will be presented with their respective examples, seeking to have a base for more advanced studies in the future. Also, some applications of population models will be displayed, such as the rabbit reproduction model (Fibonacci), the calculation of the infant mortality rate in Brazil, a projection of internet users in Brazil from 2011 to 2018, and, finally a system that models the amount of Bisons in North America.