29 citations · 34 across the 3 of their papers we have counts for
9 papers · 1 filter
Uniform upper bound for the number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
The existence of a uniform upper bound for the maximum number of limit cycles of planar piecewise linear differential systems with two zones separated by a straight line has been s…
Lyapunov coefficients for monodromic tangential singularities in Filippov vector fields
Douglas D. Novaes, Leandro A. Silva
In planar analytic vector fields, a monodromic singularity can be distinguished between a focus or a center by means of the Lyapunov coefficients, which are given in terms of the p…
Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve
Kamila da S. Andrade, Oscar A. R. Cespedes, Dayane R. Cruz +1
In this paper, we are interested in providing lower estimations for the maximum number of limit cycles that planar piecewise linear differential systems with two zones separ…
A new simple proof for Lum-Chua's conjecture
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
The already proved Lum-Chua's conjecture says that a continuous planar piecewise linear differential system with two zones separated by a straight line has at most one limit cycle.…
Study of periodic orbits in periodic perturbations of planar reversible Filippov systems having a two-fold cycle
Douglas D. Novaes, Tere M. Seara, Marco A. Teixeira +1
We study the existence of periodic solutions in a class of planar Filippov systems obtained from non-autonomous periodic perturbations of reversible piecewise smooth differential s…
Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold
Jéfferson L. R. Bastos, Claudio A. Buzzi, Jaume Llibre +1
We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert num…