Vibrational resonance in a harmonically trapped potential system

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 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 inhomogeneous medium with periodic dissipation

“…In what follows, we will focus on a form of vibrational resonance (VR). In systems with linear damping, VR has already been widely investigated [38][39][40][41][42][43][44][45] following an early study by Landa and McClintock [36]. The results have shed light on the contributions to the effective potential of the various components of the high frequency signal [27], as well as the roles played by system parameters such as delay and fractional order terms in the induction, enhancement and control of VR [46][47][48][48][49][50][51].…”