Occurrence of Vibrational resonance in an oscillator with an asymmetric Toda potential

Kolebaje, O. and Popoola, O.O. and Vincent, U.E. (2021) Occurrence of Vibrational resonance in an oscillator with an asymmetric Toda potential. Physica D: Nonlinear Phenomena, 419. ISSN 0167-2789

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Vibrational resonance (VR) is a phenomenon wherein the response of a nonlinear oscillator driven by biharmonic forces with two different frequencies, ω and Ω, such that Ω≫ω, is enhanced by optimizing the parameters of high-frequency driving force. In this paper, an counterintuitive scenario in which a biharmonically driven nonlinear oscillator does not vibrate under the well known VR conditions is reported. This behaviour was observed in a system with an integrable and asymmetric Toda potential driven by biharmonic forces in the usual VR configuration. It is shown that with constant dissipation and in the presence of biharmonic forces, VR does not take place, whereas with nonlinear displacement-dependent periodic dissipation multiple VR can be induced at certain values of high-frequency force parameters. Theoretical analysis are validated using numerical computation and Simulink implementation in MATLAB. Finally, the regime in parameter space of the dissipation for optimum occurrence of multiple VR in the Toda oscillator was estimated. This result would be relevant for experimental applications of dual-frequency driven laser models where the Toda potential is extensively employed.

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Journal Article
Journal or Publication Title:
Physica D: Nonlinear Phenomena
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This is the author’s version of a work that was accepted for publication in Physica D. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, 419, 2021 DOI: 10.1016/j.phys.2021.132853
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23 Mar 2021 16:15
Last Modified:
21 Sep 2023 03:04