Examinando por Autor "Seoane, Jesús Miguel"

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Fractional damping enhances chaos in the nonlinear Helmholtz oscillator
(SpringerLink, 2020-11-23) Ortiz, Adolfo; Yang, Jianhua; Seoane, Jesús Miguel; Coccolo Bosio, Mattia Tommaso; Fernandez Sanjuán, Miguel Ángel
The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional-order damping. For that purpose, we use the Grünwald–Letnikov fractional derivative algorithm in order to get the numerical simulations. Here, we investigate the effect of taking the fractional derivative in the dissipative term in function of the parameter . Our main findings show that the trajectories can remain inside the well or can escape from it depending on which plays the role of a control parameter. Besides, the parameter is also relevant for the creation or destruction of chaotic motions. On the other hand, the study of the escape times of the particles from the well, as a result of variations of the initial conditions and the undergoing force F, is reported by the use of visualization techniques such as basins of attraction and bifurcation diagrams, showing a good agreement with previous results. Finally, the study of the escape times versus the fractional parameter shows an exponential decay which goes to zero when is larger than one. All the results have been carried out for weak damping where chaotic motions can take place in the non-fractional case and also for a stronger damping (overdamped case), where the influence of the fractional term plays a crucial role to enhance chaotic motions. We expect that these results can be of interest in the field of fractional calculus and its applications.
Transient chaos under coordinate transformations in relativistic systems
(American Physical Society, 2020-06-23) García López, Álvaro; Sánchez Fernández, Diego; Seoane, Jesús Miguel; Fernández Sanjuán, Miguel Ángel
We use the Hénon-Heiles system as a paradigmatic model for chaotic scattering to study the Lorentz factor effects on its transient chaotic dynamics. In particular, we focus on how time dilation occurs within the scattering region by measuring the time with a clock attached to the particle. We observe that the several events of time dilation that the particle undergoes exhibit sensitivity to the initial conditions. However, the structure of the singularities appearing in the escape time function remains invariant under coordinate transformations. This occurs because the singularities are closely related to the chaotic saddle. We then demonstrate using a Cantor like set approach that the fractal dimension of the escape time function is relativistic invariant. In order to verify this result, we compute by means of the uncertainty dimension algorithm the fractal dimensions of the escape time functions as measured with an inertial frame and a frame comoving with the particle. We conclude that, from a mathematical point of view, chaotic transient phenomena are equally predictable in any reference frame and that transient chaos is coordinate invariant.