Sobre a estabilidade estrutural e regularizações de campos de vetores descontínuos

• Main Author: Jorge, Ronan Felipe [UNESP]
• Publication Date: 2016
• Format: Master thesis
• Language: por
• Source: Repositório Institucional da UNESP
• Download full: http://hdl.handle.net/11449/137852
• topic: Discontinuous systems; Regularization; Structural stability; Sistemas descontínuos; Regularização; Estabilidade Estrutural

The concept of structural stability was introduced into the studies of continuous dynamical systems by Andronov and Pontryagin (1937). In 1988, after investigating oscillators with Coulomb friction and differential equations with discontinuous right-hand sides, Filippov developed a nomenclature to the study of discontinuous dynamical systems. Since then, researches have been trying to analyze the structural stability of discontinuous dynamical systems by different methods. One of these methods is to transform, without changing the structure of vector fields, these discontinuous systems in continuous systems where the study of structural stability is already known. This transformation, also known as regularization, can be developed in various ways. This work aims at presenting a regularization method using a transition function of vector fields Z in the plane with a discontinuous set S basing in regularization method presented by Sotomayor and Teixeira (1996) in their article, and, also to do a short study about structural stability in regularized vector fields using this method.