Policiclos em sistemas de Filippov planares
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2023-07-27
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Universidade Federal de Goiás
Resumo
In this work, we study the local structure of planar Filippov systems around low codi mension Σ−singularities and we analyze systems presenting polycycles passing through
Σ−singularities. In this way, we analyze Poincaré maps (associated with such polycycles)
and determine bifurcation diagrams of Filippov systems around these minimal sets. More
specifically, we study the generic bifurcation of a Filippov system around a global con nection passing through a visible fold-regular singularity, the so-called critical crossing
cycle and we show that, under smale pertubations, such connection breaks originating
étther a sliding cycle or a crossing limit cycle. We also study a planar Filippov system
model around a certain Σ−singularity called Fold-Cusp, where a fold and a cusp meet
and we show the existence of a critical crossing cycle bifurcations from such singularity
in an unfolding of this system. In addition, we exhibit the bifurcation diagram of this
unfolding.
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Citação
SOUZA, A. C. Policiclos em sistemas de Filippov planares. 2023. 79 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2023.