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Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems
(2020-04-01)
We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov ...
Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations
(Belgian Mathematical Soc Triomphe, 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 ...
Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations
(Belgian Mathematical Soc Triomphe, 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 ...
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 Bifurcating from an Invisible Fold–Fold in Planar Piecewise Hamiltonian Systems
(2020-01-01)
The aim of this article is twofold. Firstly, we study the existence of limit cycles in a family of piecewise smooth vector fields corresponding to an unfolding of an invisible fold–fold singularity. More precisely, given ...
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 ...
ON THREE-PARAMETER FAMILIES of FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY
(World Scientific Publ Co Pte Ltd, 2014)
ON THREE-PARAMETER FAMILIES OF FILIPPOV SYSTEMS - THE FOLD-SADDLE SINGULARITY
(World Scientific Publ Co Pte LtdSingaporeSingapura, 2012)
Basin of attraction of a cusp-fold singularity in 3D piecewise smooth vector fields
(Elsevier B.V., 2014-10-01)
Generic one-parameter families of piecewise smooth vector fields on R-3 presenting the so-called cusp-fold singularity are studied. The bifurcation diagrams are exhibited and the asymptotic and structural stabilities are ...