Policiclos em sistemas de Filippov planares - Souza, Alessandra Carlos de (2023)
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.