Probing a Noisy Oscillator System

2003 ◽  
Vol 03 (03) ◽  
pp. L341-L348 ◽  
Author(s):  
J. A. Acebrón ◽  
W.-J. Rappel ◽  
A. R. Bulsara
Keyword(s):  
Coupling Strength ◽  
Low Frequency ◽  
Nonlinear Oscillators ◽  
Sinusoidal Signal ◽  
Resonance Phenomenon ◽  
Probe Signal ◽  
Oscillator System ◽  
Resonance Behavior ◽  
Squid System

We examine the effect of adding a sinusoidal signal to a system of coupled noisy nonlinear oscillators. When the frequency of this "probe" signal is close to the frequency of the unprobed system we observe a resonance behavior, enabling us to determine the underlying frequency of the noisy system. Furthermore, in the prototype SQUID system we consider here, we find that the frequency of the underlying solution decreases with increasing coupling strength. Combining this finding with the resonance phenomenon we discuss ways to enhance the sensitive of SQUIDs to weak low frequency signals.

Resonance Behavior of Low Frequency Metamaterial Cells

2020 ◽  
Author(s):  
Daniel Barth ◽  
Cong Cheng ◽  
Ahmed H. Darrat ◽  
Farzad Farajizadeh ◽  
D. Mahinda Vilathgamuwa ◽  
...  
Keyword(s):  
Low Frequency ◽  
Resonance Behavior

CLASSICAL-LIKE RESONANCE INDUCED BY NOISE IN A FITZHUGH–NAGUMO NEURON MODEL

1999 ◽  
Vol 09 (12) ◽  
pp. 2295-2303 ◽  
Author(s):  
S. RIPOLL MASSANÉS ◽  
C. J. PÉREZ VICENTE
Keyword(s):  
High Frequency ◽  
Interspike Interval ◽  
Low Frequency ◽  
Resonance Phenomenon ◽  
Characteristic Time Scale ◽  
Wide Range ◽  
External Stimuli ◽  
Interspike Interval Distribution ◽  
Stochastic Resonance Phenomenon ◽  
Interval Distribution

We have studied the stochastic behavior of Fitzhugh–Nagumo neuron-like model (FN) induced by subthreshold external stimuli. Our analysis based on three standard measures: the power spectrum, interspike interval distribution (ISI) and autocorrelation function shows that it is possible to define a characteristic time scale which can be identified in the response of the system for a wide range of frequencies. In contrast to previous studies we have focused our attention on high frequency signals which could be of interest for real systems such as nervous fibers in the auditory system. We report behaviors which resemble those of classical deterministic oscillators but never the stochastic resonance phenomenon typical of low frequency signals.

Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

scholarly journals Multiple Hysteresis Jump Resonance in a Class of Forced Nonlinear Circuits and Systems

2020 ◽  
Vol 30 (15) ◽  
pp. 2050258
Author(s):  
Maide Bucolo ◽  
Arturo Buscarino ◽  
Luigi Fortuna ◽  
Mattia Frasca
Keyword(s):  
Frequency Response ◽  
Design Strategy ◽  
Nonlinear Circuits ◽  
Resonance Phenomenon ◽  
New Class ◽  
Resonance Behavior ◽  
Type Of Behavior

In this paper, a new class of systems with nonclassical jump resonance behavior is presented. Although jump resonance has been widely studied in the literature, this contribution refers to systems presenting a multiple hysteresis jump resonance phenomenon, meaning that the frequency response of the system presents more hysteresis windows nested within the same range of frequency. The analytical conditions for observing this type of behavior are derived and a design strategy to obtain multiple hysteresis jump resonance in circuits and systems presented.

Control of amplitude death by coupling range in a network of fractional-order oscillators

2020 ◽  
Vol 34 (31) ◽  
pp. 2050303
Author(s):  
Rui Xiao ◽  
Zhongkui Sun
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Coupling Strength ◽  
Low Frequency ◽  
System Size ◽  
Coupled Systems ◽  
Amplitude Death ◽  
Function Relationship ◽  
The Relationship

We investigate the oscillating dynamics in a ring of network of nonlocally delay-coupled fractional-order Stuart-Landau oscillators. It is concluded that with the increasing of coupling range, the structures of death islands go from richness to simplistic, nevertheless, the area of amplitude death (AD) state is expanded along coupling delay and coupling strength directions. The increased coupling range can prompt the coupled systems with low frequency to occur AD. When system size varies, the area of death islands changes periodically, and the linear function relationship between periodic length and coupling range can be deduced. Thus, one can modulate the oscillating dynamics by adjusting the relationship between coupling range and system size. Furthermore, the results of numerical simulations are consistent with theoretical analysis.

Hysteresis and nonlinear detuning in a spatial-resonance phenomenon

1973 ◽  
Vol 61 (2) ◽  
pp. 401-413
Author(s):  
Ian Huntley ◽  
Ronald Smith
Keyword(s):  
Free Surface ◽  
Experimental Work ◽  
Alternative Model ◽  
Pressure Field ◽  
Low Frequency ◽  
Theoretical Description ◽  
Resonance Phenomenon ◽  
Theoretical Problem ◽  
Frequency Wave ◽  
Spatial Resonance

The experimental work of Franklin, Price & Williams (1973) shows that for moderately large driving amplitudes there are features of spatial resonance that are not predicted by the model representation of Mahony & Smith (1972). We here derive an alternative model, which remains valid for moderately large driving amplitudes, and we are able to obtain a theoretical description of both hysteresis and nonlinear detuning of the low frequency wave response. An experiment in which surface waves were generated by a sinusoidal pressure field at the free surface (and which corresponds almost exactly to the theoretical problem) was conducted in order to test these predictions.

Optimizing the Electrical Power in an Energy Harvesting System

2015 ◽  
Vol 25 (12) ◽  
pp. 1550171 ◽  
Author(s):  
Mattia Coccolo ◽  
Grzegorz Litak ◽  
Jesús M. Seoane ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Energy Harvesting ◽  
Kinetic Energy ◽  
High Frequency ◽  
Energy Harvester ◽  
Electrical Power ◽  
Low Frequency ◽  
Electrical Energy ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Energy Harvesting System

In this paper, we study the vibrational resonance (VR) phenomenon as a useful mechanism for energy harvesting purposes. A system, driven by a low frequency and a high frequency forcing, can give birth to the vibrational resonance phenomenon, when the two forcing amplitudes resonate and a maximum in amplitude is reached. We apply this idea to a bistable oscillator that can convert environmental kinetic energy into electrical energy, that is, an energy harvester. Normally, the VR phenomenon is studied in terms of the forcing amplitudes or of the frequencies, that are not always easy to adjust and change. Here, we study the VR generated by tuning another parameter that is possible to manipulate when the forcing values depend on the environmental conditions. We have investigated the dependence of the maximum response due to the VR for small and large variations in the forcing amplitudes and frequencies. Besides, we have plotted color coded figures in the space of the two forcing amplitudes, in which it is possible to appreciate different patterns in the electrical power generated by the system. These patterns provide useful information on the forcing amplitudes in order to produce the optimal electrical power.

Studies on the signal amplification in weighted and unweighted small-world networks

2017 ◽  
Vol 31 (04) ◽  
pp. 1750021
Author(s):  
Yang Gao ◽  
Jianjun Wang ◽  
Fuqiu Ma
Keyword(s):  
Coupling Strength ◽  
Gaussian White Noise ◽  
Network Connectivity ◽  
Small World ◽  
Weak Signal ◽  
Small World Networks ◽  
Weighted Networks ◽  
Resonance Behavior ◽  
Optimal Values ◽  
Temporal Periodicity

Weighted and unweighted networks composed of coupled bistable oscillators with small-world topology are investigated under the co-presence of a weak signal and multiplicative Gaussian white noise. As the noise intensity is adjusted to one or two optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of stochastic resonance (SR) or stochastic bi-resonance (SBR). The resonance behavior is strongly-dependent on the coupling strength in both networks. At a weak coupling, SR more likely takes place; whereas at a strong coupling, SBR is prone to occur. Compared with unweighted networks, the span of coupling strength for SBR is narrower in weighted networks. In addition, the weak signal cannot be amplified so effectively in the weighted networks as in the unweighted networks, attributing to the weakening effect of the link weight on the coupling between oscillators and the heterogeneity of the whole network connectivity caused by the weight distribution.

scholarly journals Resonance Effects in the NASA Transonic Flutter Cascade Facility

2003 ◽  
Author(s):  
J. Lepicovsky ◽  
V. R. Capece ◽  
C. T. Ford
Keyword(s):  
Experimental Data ◽  
Low Frequency ◽  
Separated Flow ◽  
The Self ◽  
Resonance Phenomenon ◽  
Ensemble Averaging ◽  
Resonance Effects ◽  
Transonic Flutter ◽  
Blade Flutter ◽  
Mach Numbers

Investigations of unsteady pressure loadings on the blades of fans operating near the stall flutter boundary are carried out under simulated conditions in the NASA Transonic Flutter Cascade facility (TFC). It has been observed that for inlet Mach numbers of about 0.8, the cascade flowfield exhibits intense low-frequency pressure oscillations. The origins of these oscillations were not clear. It was speculated that this behavior was either caused by instabilities in the blade separated flow zone or that it was a tunnel resonance phenomenon. It has now been determined that the strong low-frequency oscillations, observed in the TFC facility, are not a cascade phenomenon contributing to blade flutter, but that they are solely caused by the tunnel resonance characteristics. Most likely, the self-induced oscillations originate in the system of exit duct resonators. For sure, the self-induced oscillations can be significantly suppressed for a narrow range of inlet Mach numbers by tuning one of the resonators. A considerable amount of flutter simulation data has been acquired in this facility to date, and therefore it is of interest to know how much this tunnel self-induced oscillations influences the experimental data at high subsonic Mach numbers since this facility is being used to simulate flutter in transonic fans. In short, can this body of experimental data still be used reliably to verify computer codes for blade flutter and blade life predictions? To answer this question a study on resonance effects in the NASA TFC facility was carried out. The results, based on spectral and ensemble averaging analysis of the cascade data, showed that the interaction between self-induced oscillations and forced blade motion oscillations is very weak and can generally be neglected. The forced motion data acquired with the mistuned tunnel, when strong self-induced oscillations were present, can be used as reliable forced pressure fluctuations provided that they are extracted from raw data sets by an ensemble averaging procedure.

scholarly journals Low-frequency oscillations in coupled phase oscillators with inertia

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Huihui Song ◽  
Xuewei Zhang ◽  
Jinjie Wu ◽  
Yanbin Qu
Keyword(s):  
Phase Fluctuation ◽  
Low Frequency ◽  
Power Grids ◽  
Kuramoto Model ◽  
Resonance Phenomenon ◽  
Forced Oscillations ◽  
Propagation Path ◽  
Phase Oscillators ◽  
Magnitude Distribution ◽  
Periodically Driven

AbstractThis work considers a second-order Kuramoto oscillator network periodically driven at one node to model low-frequency forced oscillations in power grids. The phase fluctuation magnitude at each node and the disturbance propagation in the network are numerically analyzed. The coupling strengths in this work are sufficiently large to ensure the stability of equilibria in the unforced system. It is found that the phase fluctuation is primarily determined by the network structural properties and forcing parameters, not the parameters specific to individual nodes such as power and damping. A new “resonance” phenomenon is observed in which the phase fluctuation magnitudes peak at certain critical coupling strength in the forced system. In the cases of long chain and ring-shaped networks, the Kuramoto model yields an important but somehow counter-intuitive result that the fluctuation magnitude distribution does not necessarily follow a simple attenuating trend along the propagation path and the fluctuation at nodes far from the disturbance source could be stronger than that at the source. These findings are relevant to low-frequency forced oscillations in power grids and will help advance the understanding of their dynamics and mechanisms and improve the detection and mitigation techniques.

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