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Generic bifurcations of planar filippov systems via geometric singular perturbations
(2011-01-01)
In this paper we deal with non-smooth vector fields on the plane. We prove that the analysis of their local behavior around certain typical singularities can be treated via singular perturbation theory. In fact, after a ...
Limit cycles of discontinuous piecewise polynomial vector fields
(2017-05-01)
When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we ...
Center boundaries for planar piecewise-smooth differential equations with two zones
(2017-01-01)
This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary ...
ON THREE-PARAMETER FAMILIES of FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY
(World Scientific Publ Co Pte Ltd, 2012-12-01)
This paper presents results concerning bifurcations of 2D piecewise-smooth vector fields. In particular, the generic unfoldings of codimension-three fold-saddle singularities of Filippov systems, where a boundary-saddle ...
ON THREE-PARAMETER FAMILIES of FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY
(World Scientific Publ Co Pte Ltd, 2012-12-01)
This paper presents results concerning bifurcations of 2D piecewise-smooth vector fields. In particular, the generic unfoldings of codimension-three fold-saddle singularities of Filippov systems, where a boundary-saddle ...
Equações diferenciais ordinárias não suaves autônomas e não autônomasAutonomous and non autonomous non smooth ordinary differential equations
(Universidade Estadual Paulista (Unesp), 2016)
ON THREE-PARAMETER FAMILIES of FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY
(World Scientific Publ Co Pte Ltd, 2014)
Limit cycles bifurcating from discontinuous centres
(Oxford Univ Press, 2017-08-01)
In this article, we study limit cycles in discontinuous piecewise linear vector fields in R-2 and R-3. More precisely, we address the problem of understanding the dynamics around a degenerated two-fold singularity in R-2 ...
Equações diferenciais ordinárias não suaves autônomas e não autônomas
(Universidade Estadual Paulista (Unesp), 2016-05-20)
Nesta tese estudamos sistemas dinâmicos não suaves autônomos e não autônomos. Consideramos inicialmente sistemas quadráticos positivamente limitados autônomos planares e damos condições sobre os campos para que o sistema ...
Planar reversible vector fields, averaging theory and polycycles in non-smooth vector fields
(Universidade Estadual Paulista (Unesp), 2021-06-28)
Neste trabalho veremos os retratos de fase, no disco de Poincaré, das formas normais locais das singularidades simétricas dos campos reversíveis do tipo (2; 0) e (2; 1) de baixa codimensão; uma aplicação da Teoria da Média ...