Analysis of vibrational resonance in bi-harmonically driven plasma

Abstract

The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven two-fluid plasma model with nonlinear dissipation. An equation for the slow oscillations of the system is analytically derived in terms of the parameters of the fast signal using the method of direct separation of motion. The presence of a high frequency externally applied electric field is found to significantly modify the system's dynamics, and consequently, induce VR. The origin of the VR in the plasma model has been identified, not only from the effective plasma potential but also from the contributions of the effective nonlinear dissipation. Beside several dynamical changes, including multiple symmetry-breaking bifurcations, attractor escapes, and reversed period-doubling bifurcations, numerical simulations also revealed the occurrence of single and double resonances induced by symmetry breaking bifurcations.

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].…”

Vibrational resonance in an inhomogeneous medium with periodic dissipation

“…Using a parameter of the nonlinear dissipation, in this case λ, as the bifurcation parameter we first examine the bifurcation structure. It is well known that in nonlinear systems, resonance curves are closely linked to the underlying bifurcation structure [27,53,60,61]. In particular, Koz lowski et al [61] and Roy-Layinde et al [53] have shown that symmetry-breaking (sb) bifurcations occur between resonances.…”

“…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]. However, relatively little attention has been paid to the possible contribution of nonlinear dissipation to the occurrence of VR, as described very recently for a prestressed beam fixed at both ends [52] and for a biharmonically driven plasma [53]. VR is usually discussed in terms of a slowly-driven system's response to variations in the parameters of an imposed fast periodic signal.…”

“…VR is usually discussed in terms of a slowly-driven system's response to variations in the parameters of an imposed fast periodic signal. It has been shown, however, that signal-enhancement or -suppression is also possible through variation of the bifurcation parameters of the model in the presence of a bi-harmonic drive, within appropriate parameter regimes [53,54]. This result suggests that internal parameters like frictional inhomogeneity, or nonlinear dissipation, may also play independent or contributory roles in the occurrence of VR.…”

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].…”