7 papers
Local bifurcations in a class of piecewise-smooth Filippov systems with a nonregular switching curve via a nonlinear double regularization process
Claudio A. Buzzi, Yagor Romano Carvalho
We are interested in analyzing the preservation of bifurcations in a class of piecewise smooth vector fields with a nonregular switching set under a smoothing process that approxim…
Crossing limit cycles in piecewise smooth Kolmogorov systems: an application to Palomba's model
Yagor Romano Carvalho, Luiz Fernando da Silva Gouveia, Oleg Makarenkov
In this paper, we study the number of isolated crossing periodic orbits, so-called crossing limit cycles, for a class of piecewise smooth Kolmogorov systems defined in two zones se…
Study of Poincare map and limit cycles for non-smooth Welander's system
Yagor Romano Carvalho, Luiz F. S. Gouveia, Richard Mcgehee
In this work, our primary goal is to study the Poincare map and the existence of limit cycles for Welander's model that describes ocean convection. Welander developed two versions…
New lower bound for the Hilbert number in low degree Kolmogorov systems
Yagor Romano Carvalho, Leonardo P. C. Da Cruz, Luiz F. S. Gouveia
Our main goal in this paper is to study the number of small-amplitude isolated periodic orbits, so-called limit cycles, surrounding only one equilibrium point a class of polynomial…
Crossing limit cycles of planar discontinuous piecewise differential systems formed by isochronous centers
Claudio A. Buzzi, Yagor Romano Carvalho, Jaume Llibre
These last years an increasing interest appeared for studying the planar discontinuous piecewise differential systems motivated by the rich applications in modelling real phenomena…
Limit cycles for some families of smooth and non-smooth planar systems
Claudio A. Buzzi, Yagor Romano Carvalho, Armengol Gasull
In this paper, we apply the averaging method via Brouwer degree in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to…
The local period function for Hamiltonian systems with applications
Claudio A. Buzzi, Yagor Romano Carvalho, Armengol Gasull
In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of an…