Examinando por Autor "Seoane, Jesús"

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Fractional damping effects on the transient dynamics of the Duffing oscillator
(Elsevier, 2023-02) Coccolo, Mattia; Seoane, Jesús; Lenci, Stefano; Sanjuán, Miguel Ángel
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped and overdamped regimes. In both we have studied the relation between the fractional parameter, the amplitude of the oscillations and the times to reach the asymptotic behavior, called asymptotic times. In the overdamped regime, the study shows that, also here, there are oscillations for fractional order derivatives and their amplitudes and asymptotic times can suddenly change for small variations of the fractional parameter. In addition, in this latter regime, a resonant-like behavior can take place for suitable values of the parameters of the system. These results are corroborated by calculating the corresponding -factor. We expect that these results can be useful for a better understanding of fractional dynamics and its possible applications as in modeling different kind of materials that normally need complicated damping terms.
Fractional damping induces resonant behavior in the Duffing oscillator
(Elsevier, 2024-06) Coccolo, Mattia; Seoane, Jesús; Sanjuán, Miguel Ángel
The interaction between the fractional order parameter and the damping parameter can play a relevant role for introducing different dynamical behaviors in a physical system. Here, we study the Duffing oscillator with a fractional damping term. Our findings show that for certain values of the fractional order parameter, the damping parameter, and the forcing amplitude high oscillations amplitude can be induced. This phenomenon is due to the appearance of a resonance in the Duffing oscillator only when the damping term is fractional.
Phase control of escapes in the fractional damped Helmholtz oscillator
(Elsevier, 2024-06) Coccolo, Mattia; Seoane, Jesús; Lenci, Stefano; Sanjuán, Miguel Ángel
We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase control technique into a parametric term, a feature commonly encountered in real-world situations. In the non-fractional case it has been shown that, a phase difference of \pi, is the optimal value to avoid the escapes of the particles from the potential well. Here, our investigation focuses on understanding when particles escape, considering both the phase difference \phi and the fractional parameter \alpha as control parameters. Our findings unveil the robustness of phase control, as evidenced by the consistent oscillation of the optimal \phi value around its non-fractional counterpart when varying the fractional parameter. Additionally, our results underscore the pivotal role of the fractional parameter in governing the proportion of bounded particles, even when utilizing the optimal phase.