5 papers
Generalized Pseudo-Hopf Bifurcation: Limit Cycle Position and Period
Lucas Queiroz Arakaki, Douglas Novaes, Paulo Santana
We investigate planar piecewise-smooth vector fields with a discontinuity line, focusing on the bifurcation of crossing limit cycles that arise when one of the vector fields is tra…
Normally hyperbolic limit tori near monodromic singularities in 3D polynomial vector fields
Lucas Queiroz Arakaki, Luiz F. S. Gouveia, Douglas D. Novaes
We investigate the maximal number of normally hyperbolic limit tori in three-dimensional polynomial vector fields of degree , which extends the classical notion of Hilb…
Strict increase in the number of normally hyperbolic limit tori in 3D polynomial vector fields
Lucas Queiroz Arakaki, Douglas D. Novaes
The second part of Hilbert's 16th problem concerns determining the maximum number of limit cycles that a planar polynomial vector field of degree can exhibit. A natural…
Global stability of the Lengyel-Epstein systems
Lucas Queiroz Arakaki, Luis Fernando Mello, Ronisio Moises Ribeiro
We study the global (asymptotic) stability of the Lengyel-Epstein differential systems, sometimes called Belousov-Zhabotinsky differential systems. Such systems are topologically e…
On the cyclicity of persistent hyperbolic polycycles
Lucas Queiroz Arakaki, Paulo Santana
In this work we consider families of smooth vector fields having a persistent polycycle with hyperbolic saddles. We derive the asymptotic expansion of the return map associated…