Vibrational resonance in an oscillator with an asymmetrical deformable potential

Abstract

We report the occurrence of vibrational resonance (VR) for a particle placed in a nonlinear asymmetrical Remoissenet-Peyrard potential substrate whose shape is subjected to deformation. We focus on the possible influence of deformation on the occurrence of vibrational resonance (VR) and show evidence of deformation-induced double resonances. By an approximate method involving direct separation of the timescales, we derive the equation of slow motion and obtain the response amplitude. We validate the theoretical results by numerical simulation. Besides revealing the existence of deformation-induced VR, our results show that the parameters of the deformed potential have a significant effect on the VR and can be employed to either suppress or modulate the resonance peaks, thereby controlling the resonances. By exploring the time series, the phase space structures, and the bifurcation of the attractors in Poincaré section, we demonstrate that there are two distinct dynamical mechanisms that can give rise to deformation-induced resonances, viz: (i) monotonic increase in the size of a periodic orbit; and (ii) bifurcation from a periodic to a quasiperiodic attractor.

Quantum vibrational resonance in a dual-frequency-driven Tietz-Hua quantum well

“…It was first identified and demonstrated numerically by Landa and McClintock [9], confirmed theoretically by Gitterman [10] and by Blekhman and Landa [11,12] and detected experimentally in vertical cavity surface emitting lasers and optical systems [13][14][15][16][17]. In VR, the response of a nonlinear system to the effect of the low-frequency (LF) component of the bi-harmonic signal can be amplified by the presence of the high-frequency (HF) component when the difference between the frequencies is sufficiently large ( [7,15,[18][19][20][21][22][23][24][25][26][27][28] and references therein). The VR scenario is analogous to stochastic resonance (SR) but with the high-frequency input force taking the place of noise [29,30].…”

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

“…We will consider both the single-well and double-well configurations of the system’s potential, noting that in the latter case there is the possibility of observing multiple resonance peaks, and bearing in mind that VR occurs in systems with bistable and multistable potentials where for certain parameter regimes multiple resonance can be obtained [1] , [13] , [14] , [18] , [55] , [61] , [62] , [135] .…”

“…The phenomenon has gained enormous research attention in the last two decades and has been extensively investigated due its several potential industrial and biomedical applications in a wide range of contexts including bistable systems [45] , [46] , [47] , [48] , multistable systems [19] , [49] , systems with various forms of potential structures [13] , [15] , linearly damped systems [1] , [50] , electrical circuits and time-delayed systems [5] , [6] , [51] , [52] , as well as plasma models [10] , [53] . Although earlier VR studies focused on the parameters of the high-frequency component of the bi-harmonic force, some recent VR research has explored the effects of parameters such as nonlinear damping/dissipation [7] , [10] , [53] , [54] , the complementary roles played by system’s innate bifurcation parameters [13] , [48] , [55] , the effect of time-delay [52] , [56] and fractional derivatives [57] , [58] , [59] , antiresonance [60] , the depth of a potential and the location of its minimum [61] , the effects of potential deformation [62] and potential roughness [53] , and mass-dependent VR [63] , amongst others. More importantly, VR has been realized experimentally in vertical cavity surface emitting lasers and optical systems [45] , [46] , [49] , [64] , [65] .…”

Weak signal enhancement by nonlinear resonance control in a forced nano-electromechanical resonator

“…2,30 considers the motion of a nonlinear oscillator in a bistable potential, subject to a lowfrequency signal and a high-frequency drive. Theoretical studies so far have mostly concentrated on studying the impact of the potential shape on the resonance 29,31,32 , or the response to multifrequency signals 33 . Interestingly, it was also noted in Gitterman 30 that one particularly important aspect of vibrational resonance was the ability to change the stability of some equilibria, or to have control over the shift of the resonance frequency.…”