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Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2
(2016-02-01)
We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class ...
On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems
(2015-11-15)
In this paper we consider the linear differential center (x,y)=(-y,x) perturbed inside the class of all discontinuous piecewise linear differential systems with two zones separated by the straight line y=0. Using the ...
Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2
(Elsevier B.V., 2015-01-01)
The main goal of this paper is to study the maximum number of limit cycles that bifurcate from the period annulus of the cubic centers that have a rational first integral of degree 2 when they are perturbed inside the class ...
Birth of limit cycles bifurcating from a nonsmooth center
(Elsevier B.V., 2014-07-01)
This paper is concerned with a codimension analysis of a two-fold singularity of piecewise smooth planar vector fields, when it behaves itself like a center of smooth vector fields (also called nondegenerate Sigma-center). ...
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 ...
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 ...
Smoothing of nonsmooth differential systems near regular-tangential singularities and boundary limit cycles
(2021-06-01)
Understanding how tangential singularities evolve under smoothing processes was one of the first problem concerning regularization of Filippov systems. In this paper, we are interested in C n -regularizations of Filippov ...
Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems
(Springer, 2014-04-01)
We study the maximum number of limit cycles that bifurcate from the periodic solutions of the family of isochronous cubic polynomial centers(x) over dot = y(-1 + 2 alpha x + 2 beta x(2)), (y) over dot = x + alpha(y(2) - ...
A limit-cycle solver for nonautonomous dynamical systemsA limit-cycle solver for nonautonomous dynamical systems
(Revista Mexicana de Física, 2009)
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 ...