Policiclos em sistemas de Filippov planares

• Autor(a) principal: Souza, Alessandra Carlos de
• Data de Publicação: 2023
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/13037
• topic: Sistemas de Filippov; Sistemas dinâmicos; Bifurcações; Policiclo; Singularidade dobra-regular; Singularidade dobra-cúspide; Filippov systems; Dynamical systems; Bifurcations; Polycycle; Fold-regular singularity; Fold-cusp singularity; CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

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.