Vibrational resonance in an inhomogeneous medium with periodic dissipation

Abstract

The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.

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

“…The analysis of resonance, especially in nonlinear systems, has received close attention in the scientific community, both pure and applied. The fundamental understanding of resonance is highly relevant to numerous practical applications in many branches of science, engineering, and medicine [1] , [5] , [6] , [7] , [8] . In general, resonance implies the matching of two or more frequencies within a system and, in most dynamical systems, it can appear in various forms when the frequency of an external driving force is matched to the natural frequency of the system, when it gives rise to an enhancement of the system’s response [1] , [8] , [9] , [10] .…”

“…The type of resonance depends largely on the matching method as well as on the nature of the external driving force that produces it [11] , [12] . Vibrational resonance, for example, occurs in dual-frequency-driven non-linear systems with distinct frequencies [7] , [8] , [9] , [10] , [13] , [14] , [15] , [16] , [17] , [18] , [19] ; stochastic resonance (SR) occurs when one of the two forces is replaced with noise of appropriate intensity [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] ; and chaotic resonance takes place when the high-frequency component of the driving force is replaced with the output from a chaotic system [29] , [30] , [31] . Other forms of resonance include coherence resonance [32] , [33] , [34] , ghost resonance [21] , [35] , [36] and autoresonance [37] , [38] , parametric resonance [39] , [40] , [41] , as well as conventional resonance in the form of harmonic, subharmonic and ultraharmonic resonances [42] , [43] , [44] .…”

“…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] .…”

Vibrational resonance in an oscillator with an asymmetrical deformable potential

“…Such amplification takes place when the response amplitude becomes minimum at the bifurcation of the effective potential. Following the foundational studies on VR [11,13,15], vibrational resonance has attracted a lot of research attention and has been reported in bistable systems [11,15,19], multistable systems [20][21][22], excitable systems [23], ratchets [24], quintic oscillators [25], overdamped systems [11,21,24], coupled oscillators [21,26], delayed systems [21,[26][27][28], asymmetric Duffing oscillators [29], fractional order damped oscillators [30][31][32], feedback networks [33], neuron models [23,34,35], a synthetic gene network [36], biological nonlinear maps [37], and systems with nonlinear dissipation [38][39][40], as well as in harmonically trapped potential systems [41]. In addition, experimental evidence for VR has been reported in bistable and multistable vertical-cavity surface-emitting lasers (VCSELs) [19,22,42,43].…”