Phenomenon Of Vibrational Resonance Research Articles

Taming vibrational resonance by transient high frequency

We investigate the phenomenon of vibrational resonance (VR) in a model of two-fluid plasma driven by biharmonic forcing. We introduce a transient high-frequency (HF) signal by implementing the control parameter τ that clips the HF in rationale with the time period of the system. We found that one can efficiently tame the emergence and characteristics of VR with the introduction of τ. We study a coupled 1D lattice and a 2D array of the model to decipher the influence of τ on VR. We derive the analytical response curve of the uncoupled model at τ=1/2 and find good congruence with the numerical results. When τ>0 reduces the influence of the HF signal, we found that the diminution of τ curtails the occurrence of VR. The study finds potential applications in the fields of engineering, physics, and biology where resonance due to vibration has to be damped.

Effects of electric field on vibrational resonance in Izhikevich neuronal systems

In this paper, based on the Izhikevich neuron model, the effects of electric field (EF) on vibrational resonance (VR) of single neuron and bidirectionally coupled neurons system are investigated. It is found that multiple vibrational resonances (MVR) can be observed in a single Izhikevich neuron model whether EF is considered or not. After the introduction of EF, the system exhibits worse MVR and local vibrational anti-resonance can be observed. In coupled neuronal system, the effect of bidirectional coupling causes MVR to disappear and the system only exhibits the phenomenon of VR. When EF is not considered, the vibrational anti-resonance is also observed. Interestingly, the introduction of EF weakens both VR and anti-resonance in the system. In addition, the effects of system parameters such as the EF strength controller and coupling strength on the Fourier coefficients are also investigated, and it is found that these parameters can also cause changes in the number of resonance peaks, resulting in vibrational bi-resonance and vibrational triple-resonance. The EF plays an important role in attenuating VR in neuronal systems. Therefore, this study can provide new insights for further control of abnormal electrical activities and information transmission in neurons.

Vibrational control and resonance of a nonlinear tilted cantilever beam under multi-harmonic low and high-frequency excitations

This paper investigates the vibrational resonance and control of the response of a nonlinear tilted cantilever beam under combined multi-harmonic low and non-resonant, high-frequency excitations. The basic system considers the first mode of vibration of a nonlinear tilted beam under parametric and direct base excitation with the frequency components locked in 2:1 ratio. Such a system is susceptible to parametric amplification of resonance, which may be detrimental for structural health in many mechanical systems. The primary objective of the research is to investigate the non-trivial effects of non-resonant high-frequency excitation on parametric amplification, vibrational resonance and chaos in the system, which, to the best of the authors’ knowledge, is not reported previously in the literature. The slow dynamic equations of the system are obtained using the method of direct partition of motion (MDPM), which is then analysed using the harmonic balance method (HBM). It has been shown that the high-frequency base excitation considerably influences the effective damping and stiffness of the system under consideration. The results of the research demonstrate that high-frequency excitation can effectively control the parametric amplification by shifting the resonance curve in the frequency axis and eliminating undesirable bifurcations by increasing the effective damping. The phenomenon of vibrational resonance has been found for specific parameter values in the presence of high-frequency base excitation. Detail parametric studies are performed to reveal the system’s rich nonlinear dynamics and bifurcations, like multiple jumps in response, dual peaks, isolated resonance response (isola), loop formation in frequency response plot, etc. The numerical results reveal that high-frequency excitation transforms chaotic responses into regular periodic responses. Direct numerical simulations are performed in MATLAB SIMULINK to validate the analytical results.

Nonlinear Resonance in a Position-Dependent Mass-Duffing Oscillator System with Monostable Potentials Driven by an Amplitude-Modulated Signal

This study examines the phenomenon of vibrational resonance (VR) in a classical positiondependent mass (PDM) system characterized by three types of single-well potentials. These potentials are influenced by an amplitude-modulated (AM) signal with $\Omega\gg\omega$. Our analysis is limited to the following parametric choices: <br> (i) $\omega_0^2$, $\beta$, $m_0$, $\lambda>0$ (type-1 single-well), <br> (ii) $\omega_0^2>0$, $\beta <0$, $2< m_0 <3$, $1< \lambda <2$ (type-2 single-well), <br> (iii) $\omega_0^2>0$, $\beta <0$, $0< m_0 <2$, $0<\lambda<1$ (type-3 single-well). <br> The system presents an intriguing scenario in which the PDM function significantly contributes to the occurrence of VR. In addition to the analytical derivation of the equation for slow motions of the system based on the high-frequency signal’s parameters using the method of direct separation of motion, numerical evidence is presented for VR and its basic dynamical behaviors are investigated. Based on the findings presented in this paper, the weak low-frequency signal within the single-well PDM system can be either attenuated or amplified by manipulating PDM parameters, such as mass amplitude ($m_0$) and mass spatial nonlinearity $\lambda$. The outcomes of the analytical investigations are validated and further supported through numerical simulations.

Vibrational Resonance and Electrical Activity Behavior of a Fractional-Order FitzHugh–Nagumo Neuron System

Making use of the numerical simulation method, the phenomenon of vibrational resonance and electrical activity behavior of a fractional-order FitzHugh–Nagumo neuron system excited by two-frequency periodic signals are investigated. Based on the definition and properties of the Caputo fractional derivative, the fractional L1 algorithm is applied to numerically simulate the phenomenon of vibrational resonance in the neuron system. Compared with the integer-order neuron model, the fractional-order neuron model can relax the requirement for the amplitude of the high-frequency signal and induce the phenomenon of vibrational resonance by selecting the appropriate fractional exponent. By introducing the time-delay feedback, it can be found that the vibrational resonance will occur with periods in the fractional-order neuron system, i.e., the amplitude of the low-frequency response periodically changes with the time-delay feedback. The weak low-frequency signal in the system can be significantly enhanced by selecting the appropriate time-delay parameter and the fractional exponent. In addition, the original integer-order model is extended to the fractional-order model, and the neuron system will exhibit rich dynamical behaviors, which provide a broader understanding of the neuron system.

Enhanced vibrational resonance by an amplitude modulated signal in a nonlinear dissipative two‐fluid plasma model

AbstractThe phenomenon of vibrational resonance is studied in a nonlinear dissipative two‐fluid plasma model with an asymmetric single‐well and double‐well potentials driven by an amplitude modulated (AM) signal. The external signal consisting of a low‐frequency () component and two high‐frequencies () and () components with . First, the approximate analytical expression for the response amplitude Q at the low frequency is obtained by means of direct separation of the slow and fast motions. We verified the theoretical results by numerical simulation using fourth‐order Runge–Kutta method and found it is in good agreement with the theoretical analysis. We show the enhanced response amplitude at the low frequency , showing more number of resonance peaks, a non‐decay of the response amplitude and hysteresis, and a jump phenomenon on the response amplitude curve due to the AM signal. In addition, we studied the effect of nonlinear dissipation on the response amplitude curve. By exploring the phase portrait and the bifurcation diagram, we explain the resonance mechanism and account for the other features of the resonance curve.

Vibrational resonance in a neuron-astrocyte coupled model.

Recent findings have revealed that not only neurons but also astrocytes, a special type of glial cells, are major players of neuronal information processing. It is now widely accepted that they contribute to the regulation of their microenvironment by cross-talking with neurons via gliotransmitters. In this context, we here study the phenomenon of vibrational resonance in neurons by considering their interaction with astrocytes. Our analysis of a neuron-astrocyte pair reveals that intracellular dynamics of astrocytes can induce a double vibrational resonance effect in the weak signal detection performance of a neuron, exhibiting two distinct wells centred at different high-frequency driving amplitudes. We also identify the underlying mechanism of this behaviour, showing that the interaction of widely separated time scales of neurons, astrocytes and driving signals is the key factor for the emergence and control of double vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Amplification of optical signals in a bistable vertical-cavity surface-emitting laser by vibrational resonance.

The paper presents the results of the experimental study of an application of the phenomenon of vibrational resonance (VR) for enhancement of the response of a bistable vertical-cavity surface-emitting laser (VCSEL) to the effect of optical modulating signals. Specifically, two different cases were investigated: (a) the control of all-optical switching caused by a modulated orthogonal optical injection from another VCSEL and (b) the amplification of autodyne signals from a vibrating diffusely reflecting surface in the self-mixing optical interferometry. It is experimentally demonstrated that an application of the phenomenon of VR in both cases studied leads to a strong amplification of the input optical signals by a factor from 10 to 200 depending on the experimental conditions with respect to the initial values. The effect of the asymmetry of a bistable potential on the amplification factor was also studied. The results obtained can be used to improve all-optical switchings for application in communication systems and enhancement of autodyne signals in self-mixing optical interferometry. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator

The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.

Weak signal enhancement by nonlinear resonance control in a forced nano-electromechanical resonator

Driven non-linear resonators can display sharp resonances or even multistable behaviours amenable to induce strong enhancements of weak signals. Such enhancements can make use of the phenomenon of vibrational resonance, whereby a weak low-frequency signal applied to a bistable resonator can be amplified by driving the non-linear oscillator with another appropriately-adjusted non-resonant high-frequency field. Here we demonstrate experimentally and theoretically a significant resonant enhancement of a weak signal by use of a vibrational force, yet in a monostable system consisting of a driven nano-electromechanical nonlinear resonator. The oscillator is subjected to a strong quasi-resonant drive and to two additional tones: a weak signal at lower frequency and a non-resonant driving at an intermediate frequency. We analyse this phenomenon in terms of coherent nonlinear resonance manipulation. Our results illustrate a general mechanism which might have applications in the fields of microwave signal amplification or sensing for instance.

Vibrational resonance in a higher-order nonlinear damped oscillator with rough potential

We examine the vibrational resonance (VR) of particles moving in a strongly nonlinear damped medium with a harmonically perturbed potential consisting of a background smooth triple-well potential superimposed by a fast oscillating periodic function and subjected to weak and high-frequency (HF) driving forces. The combined effects of the nonlinear damping inhomogeneity and roughness induced by the harmonic perturbation on the phenomenon of VR were theoretically and numerically analysed. It was found that damping inhomogeneity contributed significantly to the enhancement of resonant states, while potential roughness can be optimised by the HF signal to assist resonance enhancement. Furthermore, the traditional smooth VR shapes occurring in the absence of roughness experienced significant distortion occasioned by potential roughness manifesting as spikes that could ultimately be optimised by large amplitudes of the fast signal to energetically facilitate the potential barrier crossing process, thereby enabling VR enhancement.

Vibrational resonance in a scale-free network with different coupling schemes

Abstract We investigate the phenomenon of vibrational resonance (VR) in neural populations, whereby weak low-frequency signals below the excitability threshold can be detected with the help of additional high-frequency driving. The considered dynamical elements consist of excitable FitzHugh–Nagumo neurons connected by electrical gap junctions and chemical synapses. The VR performance of these populations is studied in unweighted and weighted scale-free networks. We find that although the characteristic network features – coupling strength and average degree – do not dramatically affect the signal detection quality in unweighted electrically coupled neural populations, they have a strong influence on the required energy level of the high-frequency driving force. On the other hand, we observe that unweighted chemically coupled populations exhibit the opposite behavior, and the VR performance is significantly affected by these network features whereas the required energy remains on a comparable level. Furthermore, we show that the observed VR performance for unweighted networks can be either enhanced or worsened by degree-dependent coupling weights depending on the amount of heterogeneity.

Analysis of vibrational resonance in bi-harmonically driven plasma.

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.

Vibrational Resonance in the Classical Morse Oscillator Driven by Narrow-Band and Wide-Band Frequency Modulated Signals

The phenomenon of vibrational resonance (VR) in the classical Morse oscillator influenced by narrow band and wide band frequency modulated signals is numerically studied. Vibrational resonance is found to occur when the amplitudes f and g and frequencies ω and Ω of the signals are varied. The dynamics of the system is studied in the presence of both signals separately. Vibrational resonance and dynamics of the system are characterized using the response amplitude and bifurcation diagram.

Vibrational resonance in adaptive small-world neuronal networks with spike-timing-dependent plasticity

The phenomenon of vibrational resonance is investigated in adaptive Newman–Watts small-world neuronal networks, where the strength of synaptic connections between neurons is modulated based on spike-timing-dependent plasticity. Numerical results demonstrate that there exists appropriate amplitude of high-frequency driving which is able to optimize the neural ensemble response to the weak low-frequency periodic signal. The effect of networked vibrational resonance can be significantly affected by spike-timing-dependent plasticity. It is shown that spike-timing-dependent plasticity with dominant depression can always improve the efficiency of vibrational resonance, and a small adjusting rate can promote the transmission of weak external signal in small-world neuronal networks. In addition, the network topology plays an important role in the vibrational resonance in spike-timing-dependent plasticity-induced neural systems, where the system response to the subthreshold signal is maximized by an optimal network structure. Furthermore, it is demonstrated that the introduction of inhibitory synapses can considerably weaken the phenomenon of vibrational resonance in the hybrid small-world neuronal networks with spike-timing-dependent plasticity.

Vibrational resonance in a Duffing system with fractional-order external and intrinsic dampings driven by the two-frequency signals

The phenomenon of vibrational resonance (VR) in a Duffing system with both fractional-order external damping and fractional-order intrinsic damping driven by the two-frequency periodic signals is investigated. It is observed that the resonance amplitude Q can be optimized by an appropriate choice of the amplitude of the high-frequency signal. The obtained relationship between VR and the fractional-orders shows that both fractional-order external damping and fractional-order intrinsic damping can induce changes of the shapes of the effective potential function and then lead to more abundant resonance behaviors than in the traditional dynamic systems.

Vibrational resonance in the FitzHugh–Nagumo system with time-varying delay feedback

In the present paper, the phenomenon of vibrational resonance in a time-varying delayed FitzHugh–Nagumo system that is driven by two-frequency periodic signals is reported. Via a numerical simulation, the periodic vibrational resonances are found to be induced by the time-varying delay feedback under the condition that the delayed feedback strength is small, and then along with the increase of the delayed feedback strength K within the slow period (i.e., the period of low-frequency signal), the single resonance turns into multiple resonances. However, if the delayed feedback strength K is big enough, the resonance no longer occurs. More interestingly, the multiple resonances can also turn into a single resonance in a cycle by modulating the amplitude F of high-frequency signal. Furthermore, both the resonance region and the resonance amplitude are found to be able to be controlled by the time-varying delay. Finally, it is found that the regular motion of the system can be enhanced by the time-varying delay feedback and then more regular motion will present if the resonance does not occur.

Vibrational resonance in groundwater-dependent plant ecosystems

We report the phenomenon of vibrational resonance in a single species and a two species models of groundwater-dependent plant ecosystems with a biharmonic oscillation (with two widely different frequencies ω and Ω, Ω≫ω) of the water table depth. In these two systems, the response amplitude of the species biomass shows multiple resonances with different mechanisms. The resonance occurs at both low- and high-frequencies of the biharmonic force. In the single species bistable system, the resonance occurs at discrete values of the amplitude g of the high-frequency component of the water table. Furthermore, the best synchronization of biomass and its carrying capacity with the biharmonic force occurs at the resonance. In the two species excitable and time-delay model, the response amplitude (Q) profile shows several plateau regions of resonance, where the period of evolution of the species biomass remains the same and the value of Q is inversely proportional to it. The response amplitude is highly sensitive to the time-delay parameter τ and shows two distinct sequences of resonance intervals with a decreasing amplitude with τ.

Bifurcation and resonance induced by fractional-order damping and time delay feedback in a Duffing system

We develop an analytical technique to investigate the phenomenon of vibrational resonance in a fractional-order Duffing system with linear time delay feedback and driven by both low frequency and high frequency periodic signals. At first, the theoretical predication of the response amplitude at the low-frequency is obtained by the method of direct separation of slow and fast motions. Then, the bifurcation analysis is carried out based on three kinds of resonance behaviors. Further, influences of the high frequency signal, the fractional-order damping and the delay parameter on the vibrational resonance are discussed by both theoretical and numerical simulations. If the value of the fractional-order is a controllable parameter, the monotonicity of the response amplitude versus the value of the fractional-order depends on the amplitude of the high-frequency signal. If the delay parameter is a controllable parameter, the response amplitude with respect to the delay parameter presents periodic or quasi-periodic pattern, and it is similar to that in the integer-order differential system with linear time delay feedback. The good agreement between the analytical and numerical results indicates the validity of the theoretical predications.

Vibrational Resonance in Fractional-Order Anharmonic Oscillators

The phenomenon of vibrational resonance in fractional-order anharmonic oscillators is investigated. Based on the method of separating slow and fast motions, the approximate solution of the response amplitude is obtained. Both analytical and numerical results show that not only the high-frequency signal but also the fractional-order damping can induce vibrational resonance. The present results provide a new way to control periodical signals in coupled systems.