Vibrational higher-order resonances in an overdamped bistable system with biharmonic excitation

Abstract

Experimental evidence of vibrational higher-order resonances in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies is reported. The phenomenon shows up in a parameter space (the dc current, the amplitude of the high-frequency signal) as well-defined structures with multiple local maxima at higher harmonics of the low-frequency signal. Such structures appear due to a strong suppression of higher harmonics for certain values of the high-frequency amplitude and the dc current. Complexity of the structures and the total number of the local maxima depend on the harmonic order k. The behavior of nonlinear distortion factor is also studied. The experimental results are in a good agreement with the numerical results which were obtained in the model of the bistable overdamped oscillator with biharmonic excitation.

Vibrational subharmonic and superharmonic resonances

“…Through a different combination of p, m and n, we can get the superharmonic frequency components such as 2ω, 3ω, 4ω, 5ω, etc., in the response. This prediction has been verified in [12,13]. If we consider the subharmonic resonance in Eq.…”

“…The VSupR at the superharmonic frequency nω where n is a positive integer and n > 1 has been reported in [12] and [13]. However, based on the analysis in Sec.…”

“…When the VR occurs at the primary frequency ω, we have the traditional VR phenomenon. When the VR occurs at the superharmonic frequency nω, where n > 1 is a positive integer number, this kind of VR was named nonlinear VR by Ghosh and Ray [12], or vibrational higher-order resonance by Chizhevsky [13]. From theoretical considerations, a resonance can not only occur at the primary frequency ω or the superharmonic frequency nω (n is a positive integer), but it may also occur at the frequencies nω/m.…”

“…Recently, Ghosh and Ray [12] and Chizhevsky [13] found that VR can also occur at the high-order frequencies. Specifically, if the low-frequency of one excitation is ω, the vibrational resonance induced by the high-frequency excitation may occur at frequencies which are multiple of the frequency ω.…”

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].…”