Sistemas descontínuos lento-rápidos e aplicações
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Data
2023-01-26
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Universidade Federal de Goiás
Resumo
In 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some unpublished results for the climatological model.
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Citação
FERNANDES, V. C. Sistemas descontínuos lento-rápidos e aplicações. 2023. 82 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2023.