On representing noise by deterministic excitations for interpreting the stochastic resonance phenomenon

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200229 ◽  
Author(s):  
V. Sorokin ◽  
I. Demidov
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Stochastic Systems ◽  
Signal To Noise Ratio ◽  
Nonlinear Damping ◽  
Resonance Phenomenon ◽  
Oscillatory Systems ◽  
Stochastic Excitations ◽  
Viable Approach ◽  
Stochastic Resonance Phenomenon

Adding noise to a system can ‘improve’ its dynamic behaviour, for example, it can increase its response or signal-to-noise ratio. The corresponding phenomenon, called stochastic resonance, has found numerous applications in physics, neuroscience, biology, medicine and mechanics. Replacing stochastic excitations with high-frequency ones was shown to be a viable approach to analysing several linear and nonlinear dynamic systems. For these systems, the influence of the stochastic and high-frequency excitations appears to be qualitatively similar. The present paper concerns the discussion of the applicability of this ‘deterministic’ approach to stochastic systems. First, the conventional nonlinear bi-stable system is briefly revisited. Then dynamical systems with multiplicative noise are considered and the validity of replacing stochastic excitations with deterministic ones for such systems is discussed. Finally, we study oscillatory systems with nonlinear damping and analyse the effects of stochastic and deterministic excitations on such systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

On the stochastic resonance phenomenon in parametrically excited systems

2018 ◽  
Vol 30 (5) ◽  
pp. 986-1003 ◽  
Author(s):  
VLADISLAV SOROKIN ◽  
ILIYA BLEKHMAN
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Stochastic Systems ◽  
Resonance Phenomenon ◽  
Deterministic Approach ◽  
Parametrically Excited ◽  
System Behaviour ◽  
Input Signals ◽  
Mass Properties ◽  
Stochastic Resonance Phenomenon

The stochastic resonance phenomenon implies “positive” changing of a system behaviour when noise is added to the system. The phenomenon has found numerous applications in physics, neuroscience, biology, medicine, mechanics and other fields. The present paper concerns this phenomenon for parametrically excited stochastic systems, i.e. systems that feature deterministic input signals that affect their parameters, e.g. stiffness, damping or mass properties. Parametrically excited systems are now widely used for signal sensing, filtering and amplification, particularly in micro- and nanoscale applications. And noise and uncertainty can be essential for systems at this scale. Thus, these systems potentially can exhibit stochastic resonance. In the present paper, we use a “deterministic” approach to describe the stochastic resonance phenomenon that implies replacing noise by deterministic high-frequency excitations. By means of the approach, we show that stochastic resonance can occur for parametrically excited systems and determine the corresponding resonance conditions.

STOCHASTIC RESONANCE OF A LINEAR SYSTEM INDUCED BY DICHOTOMOUS NOISE

2008 ◽  
Vol 22 (06) ◽  
pp. 697-708
Author(s):  
YU-RONG ZHOU ◽  
FENG GUO ◽  
SHI-QI JIANG ◽  
XIAO-FENG PANG
Keyword(s):  
Linear System ◽  
External Field ◽  
Stochastic Resonance ◽  
Linear Response ◽  
Signal To Noise Ratio ◽  
Linear Response Theory ◽  
Resonance Phenomenon ◽  
Field Frequency ◽  
Dichotomous Noise ◽  
Stochastic Resonance Phenomenon

The stochastic resonance phenomenon in a linear system subject to multiplicative and additive dichotomous noise is investigated. By the use of the linear-response theory and the properties of the dichotomous noise, the exact expressions have been found for the first two moments and the signal-to-noise ratio (SNR). It is shown that the SNR is a non-monotonic function of the correlation time of the additive dichotomous noise, and it varies non-monotonically with the bias of the external field, with the intensity and asymmetry of the multiplicative dichotomous noise, as well as with the external field frequency. Moreover, the SNR depends on the intensity of the cross noise between the multiplicative and additive dichotomous noise, as well as on the strength and asymmetry of the additive dichotomous noise.

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.

An improved adaptive stochastic resonance with general scale transformation to extract high-frequency characteristics in strong noise

2018 ◽  
Vol 32 (15) ◽  
pp. 1850185 ◽  
Author(s):  
Dawen Huang ◽  
Jianhua Yang ◽  
Jingling Zhang ◽  
Houguang Liu
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Signal To Noise Ratio ◽  
Scale Transformation ◽  
Weak Signal ◽  
Signal Features ◽  
Signal Characteristics ◽  
Periodic Signals ◽  
Sr Method ◽  
General Scale

The idea of general scale transformation is introduced in detail. Based on this idea, an improved adaptive stochastic resonance (SR) method is proposed to extract weak signal features. Different periodic signals are considered to verify the proposed method. Compared with the normalized scale transformation, the output signal-to-noise ratio (SNR) of the proposed method is increased to a greater extent. Further, the influences of some key parameters on the responses of the two methods are discussed minutely. Results show that the improved adaptive SR method with general scale transformation is obviously superior to the traditional normalized scale transformation that is used in the former literatures. For different noise intensities and time scales, the proposed approach can always obtain the optimal response of SR to enhance the weak signal characteristics.

scholarly journals Investigation of a Nonlinear Vibrational Energy Harvester in the Stochastic Resonance Regime

Proceedings ◽  
2018 ◽  
Vol 2 (13) ◽  
pp. 1092 ◽  
Author(s):  
Bruno Andò ◽  
Salvatore Baglio ◽  
Adi R. Bulsara ◽  
Vincenzo Marletta
Keyword(s):  
Stochastic Resonance ◽  
Energy Harvester ◽  
Vibrational Energy ◽  
Wide Band ◽  
Resonance Phenomenon ◽  
Sinusoidal Vibration ◽  
Sinusoidal Input ◽  
Optimal Value ◽  
Stochastic Resonance Phenomenon ◽  
Nonlinear Energy

In this paper the possibility to exploit advantageously the Stochastic Resonance phenomenon in a Nonlinear Energy Harvester to scavenge energy from wide band mechanical vibrations is experimentally demonstrated. The device is demonstrated to be capable of scavenging energy in case of a subthreshold sinusoidal vibration and a wideband noise (limited at 100 Hz) superimposed. The existence of an optimal value of the noise intensity maximizing the switching ratio of the bistable beam, then the performances, is experimentally demonstrated. The harvester is observed to generate power up to about 60 µW and 150 µW in case of a subthreshold sinusoidal input at 1 Hz and 3 Hz with a superimposed noise limited at 100 Hz.

STOCHASTIC RESONANCE IN HINDMARSH–ROSE NEURAL NETWORK WITH SMALL-WORLD CONNECTIONS

2008 ◽  
Vol 22 (30) ◽  
pp. 5365-5373 ◽  
Author(s):  
RENHUAN YANG ◽  
AIGUO SONG
Keyword(s):  
Neural Network ◽  
Stochastic Resonance ◽  
Random Network ◽  
Small World ◽  
Resonance Curve ◽  
Resonance Phenomenon ◽  
Node Degree ◽  
Regular Network ◽  
Stochastic Resonance Phenomenon ◽  
Peak Value

We study stochastic resonance (SR) in Hindmarsh–Rose (HR) neural network with small-world (SW) connections driven by external periodic stimulus, focusing on the dependence of properties of SR on the network structure parameters. It is found that, the SW neural network enhances SR compared with single neuron. By turning coupling strength c, two categories of SR were gained. With the connection-rewiring probability p increasing, the resonance curve becomes more and more sharp and the peak value increases gradually and then reaches saturation. The SW network enhances the SR peak value compared with regular network and widens resonance in ascending range compared with random network. When decreasing node degree k, the resonance range is enlarged, and the signal noise ratio (SNR) curve becomes a two peak one from a classic single peak SR curve, and then the stochastic resonance phenomenon almost disappears.

Watermark Detector Based on Stochastic Resonance Phenomenon

2013 ◽  
Vol 11 (1) ◽  
pp. 396-401
Author(s):  
Sebastian Lanfranco ◽  
Lucas Horacio Mazzini ◽  
Alfredo Eduardo Dominguez ◽  
Jorge Luis Naguil
Keyword(s):  
Stochastic Resonance ◽  
Resonance Phenomenon ◽  
Stochastic Resonance Phenomenon

An improved adaptive stochastic resonance method for improving the efficiency of bearing faults diagnosis

2017 ◽  
Vol 232 (13) ◽  
pp. 2352-2368 ◽  
Author(s):  
Dawen Huang ◽  
Jianhua Yang ◽  
Jingling Zhang ◽  
Houguang Liu
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Signal To Noise Ratio ◽  
Fault Simulation ◽  
Resonance Method ◽  
Bistable System ◽  
Scale Transformation ◽  
High Frequency Signal ◽  
Bearing Fault ◽  
Feature Information

The general scale transformation (GST) method is used in the bistable system to deal with the weak high-frequency signal submerged into the strong noisy background. Then, an adaptive stochastic resonance (ASR) method with the GST is put forward and realized by the quantum particle swarm optimization (QPSO) algorithm. Through the bearing fault simulation signal, the ASR method with the GST is compared with the normalized scale transformation (NST) stochastic resonance (SR). The results show that the efficiency of the GST method is higher than the NST in recognizing bearing fault feature information. In order to simulate the actual engineering environment, both the adaptive GST and the NST methods are implemented to deal with the same experimental signal, respectively. The signal-to-noise ratio (SNR) of the output is obviously improved by the GST method. Specifically, the efficiency is improved greatly to extract the weak high-frequency bearing fault feature information. Moreover, under different noise intensities, although the SNR is decreased versus the increase of the noise intensity, the ASR method with the GST is still better than the traditional NST SR. The proposed GST method and the related results might have referenced value in the problem of weak high-frequency feature extraction in engineering fields.

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