29 citations · 78 across the 12 of their papers we have counts for
7 papers · 1 filter
Bounding the number of limit cycles in piecewise linear differential systems: methodology and worked examples
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
In 2012, Huan and Yang introduced the first piecewise linear differential system with two zones separated by a straight line having at least three limit cycles, serving as a counte…
A succinct characterization of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
We close the problem of the existence of period annuli in planar piecewise linear differential systems with a straight line of nonsmoothness. In fact, a characterization for the ex…
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…
Uniqueness and stability of limit cycles in planar piecewise linear differential systems without sliding region
Victoriano Carmona, Fernando Fernández-Sánchez, Douglas D. Novaes
In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential sys…
Properties of Poincaré half-maps for planar linear systems and some direct applications to periodic orbits of piecewise systems
Victoriano Carmona, Fernando Fernández-Sánchez, Elisabeth García-Medina +1
This paper deals with fundamental properties of Poincaré half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincaré hal…
Saddle-node canard cycles in planar piecewise linear differential systems
Victoriano Carmona, Soledad Fernández-García, Antonio E. Teruel
By applying a singular perturbation approach, canard limit cycles exhibited by a general family of singularly perturbed planar piecewise linear (PWL) differential systems are analy…
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.…