Browsing Articles publicats (Matemàtica) by Author "Maza Sabido, Susanna"
Now showing items 1-10 of 10
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Center cyclicity of a family of quartic polynomial differential system
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Springer, 2016-09-01)In this paper we study the cyclicity of the centers of the quartic polynomial family written in complex notation as z = i z + z z (A z^2 + B z z + C z^2 ), where A,B,C. We give an upper bound for the cyclicity of any ... -
Center cyclicity of Lorenz, Chen and Lü systems
García, I. A. (Isaac A.); Maza Sabido, Susanna; Shafer, Douglas S. (Elsevier, 2018-11-09)This work provides upper bounds on the cyclicity of the centers on center manifolds in the well-known Lorenz family, and also in the Chen and Lü families. We prove that at most one limit cycle can be made to bifurcate from ... -
Cyclicity of a simple focus via the vanishing multiplicity of inverse integrating factors
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Elsevier, 2013)First we provide new properties about the vanishing multiplicity of the inverse integrating factor of a planar analytic differential system at a focus. After we use this vanishing multiplicity for studying the cyclicity ... -
Cyclicity of polynomial nondegenerate centers on center manifolds
García, I. A. (Isaac A.); Maza Sabido, Susanna; Shafer, Douglas S. (Elsevier, 2018-11-09)We consider polynomial families of ordinary differential equations on $\R^3$, parametrized by the admissible coefficients, for which the origin is an isolated singularity at which the linear part of the system has one ... -
On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (IOP Publishing, 2018-11-21)In this work we consider real analytic functions $d(z,\la,\e)$, where $d : \Omega \times \mathbb{R}^p \times I \to \Omega$, $\Omega$ is a bounded open subset of $\R$, $I \subset \mathbb{R}$ is an interval containing the ... -
On the periodic orbit bifurcating from a Hopf bifurcation in systems with two slow and one fast variables
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Elsevier, 2014)The Hopf bifurcation in slow-fast systems with two slow variables and one fast variable has been studied recently, mainly from a numerical point of view. Our goal is to provide an analytic proof of the existence of the ... -
Period annulus of the harmonic oscillator with zero cyclicity under perturbations with a homogeneous polynomial field
García, I. A. (Isaac A.); Maza Sabido, Susanna (Bolyai Institute. University of Szeged; Hungarian Academy of Sciences, 2019-01-14)In this work we prove, using averaging theory at any order in the small perturbation parameter, that the period annulus of the harmonic oscillator has cyclicity zero (no limit cycles bifurcate) when it is perturbed by any ... -
Periodic orbits in Hyperchaotic Chen systems
Maza Sabido, Susanna (Texas State University, 2015)In this work, we show a zero-Hopf bifurcation in a Hyperchaotic Chen system. Using averaging theory, we prove the existence of two periodic orbits bifurcating from the zero-Hopf equilibria located at the origin of ... -
The Hopf cyclicity of the centers of a class of quintic polynomial vector fields
García, I. A. (Isaac A.); Llibre, Jaume; Maza Sabido, Susanna (Elsevier, 2015-01-20)We consider families of planar polynomial vector fields having a singularity with purely imaginary eigenvalues for which a basis of its Bautin ideal B is known. We provide an algorithm for computing an upper bound of the ... -
Vanishing set of inverse Jacobi multipliers and attractor/repeller sets
García, I. A. (Isaac A.); Giné, Jaume; Llibre, Jaume; Maza Sabido, Susanna (American Institute of Physics, 2021-01-01)In this paper we study conditions under which the zero-set of the inverse Jacobi multiplier of a smooth vector field contains its attractor/repeller compact sets. The work generalizes previous results focusing on sink ...