Fractional damping enhances chaos in the nonlinear Helmholtz oscillator
This paper aims to explore both underdamped and overdamped dynamics in the nonlinear Helmholtz oscillator with fractional-order damping. Utilizing the Grünwald–Letnikov fractional derivative algorithm, numerical simulations are conducted to investigate the impact of the fractional derivative in the...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Rey Juan Carlos |
| Repositorio: | BURJC-Digital. Repositorio Institucional de la Universidad Rey Juan Carlos |
| OAI Identifier: | oai:burjcdigital.urjc.es:10115/32165 |
| Acceso en línea: | https://hdl.handle.net/10115/32165 |
| Access Level: | acceso abierto |
| Palabra clave: | Nonlinear dynamics Fractional calculus Helmholtz oscillator Transient chaos |
| Sumario: | This paper aims to explore both underdamped and overdamped dynamics in the nonlinear Helmholtz oscillator with fractional-order damping. Utilizing the Grünwald–Letnikov fractional derivative algorithm, numerical simulations are conducted to investigate the impact of the fractional derivative in the dissipative term concerning the parameter α. Results demonstrate that trajectories may either remain within the well or escape depending on α, acting as a control parameter, and also influence the creation or suppression of chaotic motions. Visualization techniques such as basins of attraction and bifurcation diagrams are employed to analyze the escape times of particles from the well due to variations in initial conditions and external force F, consistent with prior findings. Additionally, the study reveals an exponential decay in escape times with respect to the fractional parameter α, converging to zero for α greater than one. Notably, the results are obtained for weak damping scenarios where chaotic motions occur in the non-fractional case, as well as for stronger damping situations (overdamped case), where the fractional term significantly influences chaotic behaviors. These findings hold implications for the field of fractional calculus and its practical applications. |
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