Artículos (Matemática Aplicada II)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10899

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Examinando Artículos (Matemática Aplicada II) por Autor "Amador, Andrés"

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    Acceso AbiertoArtículo
    A multiple focus-center-cycle bifurcation in 4D discontinuous piecewise linear memristor oscillators
    (Springer, 2018-12) Ponce Núñez, Enrique; Amador, Andrés; Ros Padilla, Francisco Javier; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Ministerio de Economía y Competitividad (MINECO). España; Consejería de Economía y Conocimiento, Junta de Andalucía; Pontificia Universidad Javeriana Cali-Colombia; Universidad de Sevilla. TIC130: Investigación en Sistemas Dinámicos en Ingeniería
    The dynamical richness of 4D memristor oscillators has been recently studied in several works, showing different regimes, from stable oscillations to chaos. Typically, only numerical simulations have been reported and so there is a lack of mathematical results. We focus our analysis in the existence of multiple stable oscillations in the 4D piecewise linear version of the canonical circuit proposed by Itoh and Chua (Int J Bifurc Chaos 18(11):3183–3206, 2008). This oscillator is modeled by a discontinuous piecewise linear dynamical system. By adding one parameter that stratifies the 4D dynamics, it is shown that the dynamics in each stratum is topologically equivalent to a 3D continuous piecewise linear dynamical system. Some previous results on bifurcations in such reduced system allow to detect rigorously for the first time a multiple focus-center-cycle bifurcation in a three-parameter space, leading to the appearance of a topological sphere in the original model, completely foliated by stable periodic orbits. © 2018, Springer Nature B.V.
  • Miniatura
    Acceso AbiertoArtículo
    Bifurcation set for a disregarded Bogdanov-Takens unfolding: Application to 3D cubic memristor oscillators
    (Springer Science and Business Media B.V., 2021) Amador, Andrés; Freire Macías, Emilio; Ponce Núñez, Enrique; Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI); Pontificia Universidad Javeriana Cali-Colombia; Ministerio de Economía y Competitividad de España; Consejería de Economía y Conocimiento (Junta de Andalucía)
    Motivated by the dynamical analysis of certain memristor-based oscillators, in this paper we derive the bifurcation set for a three-parametric Bogdanov-Takens unfolding that has not been previously considered in the literature (the saddle-focus-saddle case). By using several first-order Melnikov functions, we obtain for the first time analytical approximations for the bifurcation curves corresponding to homoclinic and heteroclinic connections, which along with the curves associated to local bifurcations organize the parametric regions with different qualitative phase planes. Our interest is the study of a family of 3D memristor oscillators, whose memristor characteristic function is a cubic polynomial. We show that these systems have a first integral; thus, after reducing the problem in one dimension, we can take advantage of the bifurcation set previously obtained. For a certain parameter region, the existence of closed surfaces completely foliated by periodic orbits in the original three-dimensional setting is shown. Additionally, we clarify some misconceptions that arise from the numerical simulations of these systems, emphasizing the important role played by the invariant manifolds associated to the involved first integral.