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Algebraic Limit Cycles in Piecewise Linear Differential Systems
(World Scientific Publ Co Pte Ltd, 2018-03-01)
This paper is devoted to study the algebraic limit cycles of planar piecewise linear differential systems. In particular, we present examples exhibiting two explicit hyperbolic algebraic limit cycles, as well as some ...
Existência e configuração de ciclos limites em sistemas diferenciais planares
(Universidade Federal de Santa MariaBrasilMatemáticaUFSMPrograma de Pós-Graduação em MatemáticaCentro de Ciências Naturais e Exatas, 2018-03-16)
In this dissertation, we present results on the existence of limit cycles in planar differential
systems, configuration of such cycles and the dynamics of nonlinear systems near periodic
orbits.
On the Limit Cycles for a Class of Continuous Piecewise Linear Differential Systems with Three Zones
(World Scientific Publ Co Pte Ltd, 2015-04-01)
Lima and Llibre [2012] have studied a class of planar continuous piecewise linear vector fields with three zones. Using the Poincare map, they proved that this class admits always a unique limit cycle, which is hyperbolic. ...
Limit Cycles Bifurcating from a Period Annulus in Continuous Piecewise Linear Differential Systems with Three Zones
(World Scientific Publ Co Pte Ltd, 2017-02-01)
We study a class of planar continuous piecewise linear vector fields with three zones. Using the Poincare map and some techniques for proving the existence of limit cycles for smooth differential systems, we prove that ...
LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS
(World Scientific Publ Co Pte Ltd, 2011-11-01)
We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in R(n) perturbed inside a class of discontinuous piecewise linear differential systems. Our ...
On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones
(Elsevier B.V., 2011-12-01)
We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems with two zones. Our main result shows that three is an upper bound for the ...
LIMIT CYCLES of DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS
(World Scientific Publ Co Pte Ltd, 2011-11-01)
We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in R(n) perturbed inside a class of discontinuous piecewise linear differential systems. Our ...
On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones
(Elsevier B.V., 2011-12-01)
We study the bifurcation of limit cycles from the periodic orbits of a four-dimensional center in a class of piecewise linear differential systems with two zones. Our main result shows that three is an upper bound for the ...
Limit cycles for some families of smooth and non-smooth planar systems
(Elsevier B.V., 2021-06-01)
We apply the averaging method in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our results can be ...
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 ...