The effect of the fractional derivative order on vibrational resonance in a special fractional quintic oscillator

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

“…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] .…”

Delay-induced vibrational resonance in the Rayleigh–Plesset bubble oscillator

“…Recently however, attention has also been given to other features and parameters of the system including e.g. nonlinear damping/dissipation [50,71,72], the effect of time-delay [17,88] and fractional derivatives [23,33], antiresonance [74], the depth of a potential and the location of its minimum [11], the effects of potential roughness [50] and potential deformation [87], as well as variation in mass [80]. More importantly, VR has been realized experimentally in vertical cavity surface emitting lasers and optical systems [12][13][14][15].…”

Vibrational resonances in driven oscillators with position-dependent mass

“…Following its introduction by Landa & McClintock [23] and motivated by the aforementioned potential applications, VR has now been demonstrated and analysed in a diversity of model systems theoretically, numerically and experimentally, cutting across many fields such as neuroscience, plasma physics, laser physics, acoustics and engineering. Specifically, the VR phenomenon has been investigated in bistable systems [24,28–35], multistable systems [36,37], ratchet devices [38], excitable systems [39], quintic oscillators [40–44], coupled oscillators [25,45–47], overdamped systems [30], delayed dynamical systems [44,46,48–52], asymmetric Duffing oscillators [53], fractional order oscillators [32,42,54], neural models [39,50,55–61], oscillatory networks [46,55,58–60,62–64], biological nonlinear systems [49,61,64], parametrically excited systems [34,65–69], systems with nonlinear damping [37,70–72], and deformed potential [73], disordered systems [74], quantum systems [75,76], as well as harmonically trapped and roughed potentials [72,77]. More importantly, VR has been demonstrated in experimental realizations, especially in multistable systems, arrays of hard limiters, bistable vertical-cavity surface-emitting lasers [28,29,33,78–81] and Chua circuits [82,83].…”