Bifurcação de Hopf e Aplicações

Abstract

The aim of this dissertation is to address the qualitative aspects of the Hopf bifurcation in systems of ordinary differential equations. We begin by presenting the fundamental objects and results of the theory, including concepts such as structural stability and the notion of distance between dynamical systems. Then, we discuss classical examples of bifurcations, such as saddle-node, pitchfork, and transcritical types. The main focus is placed on the Hopf bifurcation, with emphasis on its topological normal form and the main aspects related to its behavior.