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Previous issue date: 2013-03-22 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Consider a nonsmooth vector fields in R3 defined by parts on a smooth manifold of
dimension one, such that it is tangent to both sides simultaneously, in fold points, visibles
or invisibles. In this paper we study a local dynamics of the singularity type two-fold
invisible-invisible known as Teixeira singularity, revealing new scenes of bifurcations
and the nonlinear effects around the bifurcation already known, determining conditions
for the existence of invariant sets (limit cycles) and the possible existence of a set with
a nondeterministic chaos. Furthermore, we discuss the occurrence of this singularity in
switched feedback control systems and some numerical simulations are presented. / Quando um campo vetorial não suave é definido por partes, sobre uma variedade regular
de codimensão um, esse pode ser simultaneamente tangente a ambos os lados, em
pontos de dobra, visíveis ou invisíveis. Neste trabalho é estudada a dinâmica local da singularidade;
tipo dobra-dobra invisível-invisível conhecida como Singularidade Teixeira,
revelando novos cenários de bifurcações e os efeitos não lineares em torno da bifurcação
já conhecida, determinando condições para a existência de conjuntos invariantes (ciclos
limite), e a possível existência de um conjunto com uma forma não-determinística do
caos. Além disso, discute-se a ocorrência de tal singularidade em sistemas de controle
com retroalimentação comutante. Algumas simulações numéricas são apresentadas.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tede/3087 |
| Date | 22 March 2013 |
| Creators | Cespedes, Oscar Alexander Ramírez |
| Contributors | Medrado, João Carlos da Rocha |
| Publisher | Universidade Federal de Goiás, Programa de Pós-graduação em Matemática (IME), UFG, Brasil, Instituto de Matemática e Estatística - IME (RG) |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | Portuguese |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Source | reponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG |
| Rights | http://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess |
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