Mestrado em Matemática (IME)
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Navegando Mestrado em Matemática (IME) por Por Orientador "Euzébio, Rodrigo Donizete"
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Item Sistemas descontínuos lento-rápidos e aplicações(Universidade Federal de Goiás, 2023-01-26) Fernandes, Vitória Chaves; Euzébio, Rodrigo Donizete; http://lattes.cnpq.br/9213320273714493; Euzébio, Rodrigo Donizete; Tonon, Durval José; Buzzi, Claudio AguinaldoIn this work we study dynamical systems focused on two areas: discontinuous systems and singular perturbation problems. We analyze the intersection of these two areas through some theoretical results. In the first moment, we will present a theory similar to Fenichel's Theory for singularly perturbed discontinuous systems, later we will show that a system obtained via regularization can be associated with a singular perturbation problem. In addition, we will study a mathematical modeling in the area of climatology, with the objective of analyzing the bifurcations of singularities and the existence of a periodic orbit for certain specific parameters. In this model, we cannot apply Fenichel's theory, for this reason we use an ad-hoc application of Fenichel's Theory to demonstrate the desired results. Finally, we will present some unpublished results for the climatological model.Item Ciclos limite em sistemas lineares suaves por parte(Universidade Federal de Goiás, 2018-03-07) Silva, Ana Maria Alves da; Euzébio, Rodrigo Donizete; http://lattes.cnpq.br/9213320273714493; Buzzi, Claudio Aguinaldo; Tonon, Durval José; Euzébio, Rodrigo DonizeteIn this work we will study limit cycles in piecewise smooth linear systems. We begin studying the case where the separation curve is a polygonal and we give an example of a system having seven limit cycles. The existence of an arbitrary number of limit cycles is also proved for these systems, as well as an example of a system with 10 limit cycles. The existence of n limit cycles, n 2 N, is also studied through a perturbation in the separation curve. Finally, we study limit cycles in planar piecewise linear systems presenting a twofold singularity in R2, as well as limit cycles sorrounding a T-singularity.