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Creation of Limit Cycles in Piecewise Smooth Vector Fields Tangent to Nested Tori
(2021-07-01)
The main goal of this paper is to present the behavior generated by piecewise smooth vector fields tangent to foliations. We consider two smooth foliations F1 and F2 that are coupled to produce a foliation composed by ...
Structural stability and normal forms of piecewise smooth vector fields on R-3
(Kossuth Lajos Tudomanyegyetem, 2015-01-01)
The main goal of this paper is to exhibit normal forms of generic locally structurally stable piecewise smooth vector fields on R-3. Besides, we construct the homeomorphism that gives the topological equivalence between ...
Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields
(World Scientific Publ Co Pte Ltd, 2014-07-01)
In this paper, we are dealing with piecewise smooth vector fields in a 2D-manifold. In such a scenario, the main goal of this paper is to exhibit the homeomorphism that gives the topological equivalence between a codimension ...
Piecewise smooth vector fields in ℝ3 at infinity
(2014-11-25)
In this work we study the dynamics at infinity of a piecewise smooth vector fields in ℝ3. We provide conditions for the 24-parameter family to undergo a local bifurcations of codimension zero and one at infinity. These ...
Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields
(World Scientific Publ Co Pte Ltd, 2015)
Canonical Forms for Codimension One Planar Piecewise Smooth Vector Fields with Sliding Region
(2018-12-01)
This paper is devoted to exhibit canonical forms for 2D codimension one piecewise smooth vector fields. All possible orientations and codimension one scenarios were covered. Also the intrinsic objects that characterize ...
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 ...
Birth of limit cycles from a 3D triangular center of a piecewise smooth vector field
(2017-01-01)
We consider a piecewise smooth vector field in R3, where the switching set is on an algebraic variety expressed as the zero of a Morse function.We depart from a model described by piecewise constant vector fields with a ...
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 ...
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 ...