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Artículo
On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
(Elsevier, 2013-10)
Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with ...
Artículo
Limit cycles from a monodromic infinity in planar piecewise linear systems
(Elsevier, 2021-04-15)
Planar piecewise linear systems with two linearity zones separated by a straight line and with a periodic orbit at infinity are considered. By using some changes of variables and parameters, a reduced canonical form with ...
Artículo
The Focus-Center-Limit Cycle Bifurcation in Symmetric 3D Piecewise Linear Systems
(Society for Industrial and Applied Mathematics, 2005)
The birth of limit cycles in 3D (three-dimensional) piecewise linear systems for the relevant case of symmetrical oscillators is considered. A technique already used by the authors in planar systems is extended to cope ...
Artículo
Bifurcations from a center at infinity in 3D piecewise linear systems with two zones
(Elsevier, 2020-01)
We consider continuous piecewise linear systems in R3 with two zones under the assumption of having a linear center in the invariant manifold of the point at infinity. A specific conic projection is introduced, so that it ...
Artículo
The discontinuous matching of two planar linear foci can have three nested crossing limit cycles
(Universitat Autònoma de Barcelona, Servei de Publicacions, 2014)
The existence and stability of limit cycles in discontinuous piecewise linear systems obtained by the aggregation of two linear systems of focus type and having only one equilibrium point is considered. By using an adequate ...
Artículo
The boundary focus–saddle bifurcation in planar piecewise linear systems. Application to the analysis of memristor oscillators
(Elsevier, 2018-10)
Among the boundary equilibrium bifurcations in planar continuous piecewise linear systems with two zones separated by a straight line, the focus–saddle bifurcation corresponds with a one-parameter transition from a situation ...