scholarly journals MODEL REDUCTION AND STOCHASTIC RESONANCE

2002 ◽  
Vol 02 (04) ◽  
pp. 463-506 ◽  
Author(s):  
P. IMKELLER ◽  
I. PAVLYUKEVICH
Keyword(s):  
Stochastic Resonance ◽  
Continuous Time ◽  
Spectral Power ◽  
Glacial Cycles ◽  
Power Amplification ◽  
Qualitative Understanding ◽  
Paleoclimatic Data ◽  
Periodic Signals ◽  
Potential Landscape ◽  
Small Periodic

We provide a mathematical underpinning of the physically widely known phenomenon of stochastic resonance, i.e. the optimal noise-induced increase of a dynamical system's sensitivity and ability to amplify small periodic signals. The effect was first discovered in energy-balance models designed for a qualitative understanding of global glacial cycles. More recently, stochastic resonance has been rediscovered in more subtle and realistic simulations interpreting paleoclimatic data: the Dansgaard–Oeschger and Heinrich events. The underlying mathematical model is a diffusion in a periodically changing potential landscape with large forcing period. We study optimal tuning of the diffusion trajectories with the deterministic input forcing by means of the spectral power amplification measure. Our results contain a surprise: due to small fluctuations in the potential valley bottoms the diffusion — contrary to physical folklore — does not show tuning patterns corresponding to continuous time Markov chains which describe the reduced motion on the metastable states. This discrepancy can only be avoided for more robust notions of tuning, e.g. spectral amplification after elimination of the small fluctuations.

STOCHASTIC RESONANCE IN THE ISING MODEL ON A BARABÁSI–ALBERT NETWORK

2004 ◽  
Vol 18 (12) ◽  
pp. 1759-1770 ◽  
Author(s):  
A. KRAWIECKI
Keyword(s):  
Ising Model ◽  
Stochastic Resonance ◽  
Spectral Power ◽  
Strong Dependence ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ferromagnetic Phase ◽  
Periodic Signal ◽  
Power Amplification

Stochastic resonance is investigated in the Ising model with ferromagnetic coupling on a Barabási–Albert network, subjected to weak periodic magnetic field. Spectral power amplification as a function of temperature shows strong dependence on the number of nodes, which is related to the dependence of the critical temperature for the ferromagnetic phase transition, and on the frequency of the periodic signal. Double maxima of the spectral power amplification evaluated from the time-dependent magnetization are observed for intermediate frequencies of the periodic signal, which are also dependent on the number of nodes. In the thermodynamic limit, the height of the maxima decreases to zero and stochastic resonance disappears. Results of numerical simulations are in qualitative agreement with predictions of the linear response theory in the mean-field approximation.

scholarly journals Entropic stochastic resonance induced by a transverse driving force

2021 ◽  
Vol 379 (2198) ◽  
Author(s):  
L. C. Du ◽  
W. H. Yue ◽  
J. H. Jiang ◽  
L. L. Yang ◽  
M. M. Ge
Keyword(s):  
Stochastic Resonance ◽  
Driving Force ◽  
Spectral Power ◽  
Small Scale ◽  
Theme Issue ◽  
Periodic Force ◽  
Power Amplification ◽  
The Mean ◽  
Time Periodic ◽  
Noise Region

The phenomenon of entropic stochastic resonance (ESR) is investigated with the presence of a time-periodic force in the transverse direction. Simulation results manifest that the ESR can survive even if there is no static bias force in any direction, just if a transverse driving field is applied. In the weak noise region, the transverse driving force leads to a giant-suppression of the escape rate from one well to another, i.e. the entropic trapping. The increase in noise intensity will eliminate this suppression and induce the ESR phenomenon. An alternative quantity, called the mean free flying time, is also proposed to characterize the ESR as well as the conventional spectral power amplification. The ESR can be modulated conveniently by the transverse periodic force, which implies an alternative method for controlling the dynamics of small-scale systems. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

Stochastic resonance in the majority vote model on regular and small-world lattices

2017 ◽  
Vol 31 (29) ◽  
pp. 1750214
Author(s):  
A. Krawiecki
Keyword(s):  
Stochastic Resonance ◽  
Spectral Power ◽  
Majority Vote ◽  
Internal Noise ◽  
Small World ◽  
Time Dependent ◽  
Field Equations ◽  
Vote Model ◽  
Power Amplification ◽  
Mean Field Equations

The majority vote model with two states on regular and small-world networks is considered under the influence of periodic driving. Monte Carlo simulations show that the time-dependent magnetization, playing the role of the output signal, exhibits maximum periodicity at nonzero values of the internal noise parameter [Formula: see text], which is manifested as the occurrence of the maximum of the spectral power amplification; the location of the maximum depends in a nontrivial way on the amplitude and frequency of the periodic driving as well as on the network topology. This indicates the appearance of stochastic resonance in the system as a function of the intensity of the internal noise. Besides, for low frequencies and for certain narrow ranges of the amplitudes of the periodic driving double maxima of the spectral power amplification as a function of [Formula: see text] occur, i.e., stochastic multiresonance appears. The above-mentioned results quantitatively agree with those obtained from numerical simulations of the mean-field equations for the time-dependent magnetization. In contrast, analytic solutions for the spectral power amplification obtained from the latter equations using the linear response approximation deviate significanlty from the numerical results since the effect of the periodic driving on the system is not small even for vanishing amplitude.

Virtual Instrument for Weak Signal Detecting on Monostable Stochastic Resonance

2011 ◽  
Vol 279 ◽  
pp. 361-366
Author(s):  
Quan Yuan ◽  
Yan Shen ◽  
Liang Chen
Keyword(s):  
Power Spectrum ◽  
White Noise ◽  
Stochastic Resonance ◽  
Virtual Instrument ◽  
Stable System ◽  
Periodic Signal ◽  
Nonlinear Phenomenon ◽  
Weak Signal ◽  
Additive White Noise ◽  
Periodic Signals

Stochastic resonance (SR) is a nonlinear phenomenon which can be used to detect weak signal. The theory of SR in a biased mono-stable system driven by multiplicative and additive white noise as well as a weak periodic signal is investigated. The virtual instrument (VI) for weak signal detecting based on this theory is designed with LabVIEW. This instrument can be used to detect weak periodic signals which meets the conditions given and can greatly improved the power spectrum of the weak signal. The results that related to different sets of parameters are given and the features of these results are in accordance with the theory of mono-stable SR. Thus, the application of this theory in the detecting of weak signal is proven to be valid.

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 Research on Stochastic Resonance Signal’s Recovery

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Hao Wang ◽  
Jie Cao ◽  
Xiang Wei
Keyword(s):  
Stochastic Resonance ◽  
Bistable System ◽  
Signal Recovery ◽  
Weather Index ◽  
Recovery Method ◽  
Application Range ◽  
Periodic Law ◽  
Accurate Expression ◽  
Periodic Signals ◽  
System Coupling

Using stochastic resonance to detect weak periodic signals has been widely used in various fields of science, which attracts much attention of researchers due to its advantages of revealing recessive periodic laws. This paper utilized this method to seek the underlying rule of setting weather index, so we can find that how to obtain the accurate expression of original periodic law by further investigation. This paper deals with the noise-contained signal restoring on the basis of the established system coupling the inversion system and bistable system. The simulation shows that this signal recovery method inversion effect is better and the application range is wider.

scholarly journals Performance Investigation of Stochastic Resonance in Three Types of Asymmetric Bistable System Driven by Trichotomous Noise

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Si-Hai Zhao ◽  
Jiang-Ye Xu ◽  
Yu-Xiao Liu ◽  
Ze-Xing Zhao ◽  
Zhong-Shun Qin
Keyword(s):  
Stochastic Resonance ◽  
Potential Function ◽  
Signal To Noise Ratio ◽  
Bistable System ◽  
Potential Wells ◽  
Asymmetric System ◽  
Trichotomous Noise ◽  
Periodic Signals ◽  
Detection Effect ◽  
Better Than

This paper proposes a new system whose potential function is with three types of asymmetric potential wells, driven by trichotomous noise. Firstly, the three types of asymmetric bistable system are described in detail, and the changes of asymmetric bistable system potential function under different asymmetric factors are analyzed. Secondly, the effect of potential function parameters, asymmetric factor α , noise intensity D, and the probability of particle transition q is discussed, using numerical simulation. The detection effects of traditional symmetric SR and three types of asymmetric SR are observed and compared under the driving of trichotomous noise and periodic signals. The mean of signal-to-noise ratio gain is the indicator of the system's effectiveness on enhancing weak signal. The results indicate that it can make the detection effect of the asymmetric system better than that of the traditional bistable system by adjusting the parameters of the asymmetric stochastic resonance system and trichotomous noise.

Control of stochastic resonance in bistable systems by using periodic signals

2009 ◽  
Vol 18 (5) ◽  
pp. 1725-1730 ◽  
Author(s):  
Lin Min ◽  
Fang Li-Min ◽  
Zheng Yong-Jun
Keyword(s):  
Stochastic Resonance ◽  
Bistable Systems ◽  
Periodic Signals

INVESTIGATION OF STOCHASTIC RESONANCE IN MONOSTABLE SYSTEMS

2008 ◽  
Vol 18 (09) ◽  
pp. 2833-2839 ◽  
Author(s):  
N. V. AGUDOV ◽  
A. V. KRICHIGIN
Keyword(s):  
Stochastic Resonance ◽  
Output Signal ◽  
Noise Intensity ◽  
Signal To Noise Ratio ◽  
Gaussian White Noise ◽  
Periodic Signal ◽  
Signal Power ◽  
Signal To Noise ◽  
Input Noise ◽  
Power Amplification

The phenomena of stochastic resonance is studied in overdamped nonlinear monostable systems driven by a periodic signal and Gaussian white noise. It is shown that the signal power amplification as a function of input noise intensity can be different depending on nonlinearity: it can monotonically grow, decrease and it can reach a maximum at certain value of the noise intensity. Nevertheless, the output signal to noise ratio is shown to be always a decreasing function of input noise intensity.

STOCHASTIC RESONANCE IN COUPLED THRESHOLD ELEMENTS WITH INPUT SIGNALS SHIFTED IN PHASE

2000 ◽  
Vol 14 (08) ◽  
pp. 837-852
Author(s):  
A. KRAWIECKI ◽  
A. SUKIENNICKI ◽  
R. A. KOSIŃSKI
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Stochastic Resonance ◽  
Response Function ◽  
Signal To Noise Ratio ◽  
Binary Response ◽  
Signal To Noise ◽  
Input And Output ◽  
Input Signals ◽  
Periodic Signals

Stochastic resonance in a system of two coupled threshold elements (neurons) forming a small artificial neural network is investigated. The elements have either antisymmetric or logistic (binary) response function and are driven by periodic signals and independent noises. Periodic signals at their inputs have equal amplitudes and frequencies but are shifted in phase. Depending on the response function and the phase shift, enhancement of stochastic resonance in individual elements, characterized by the output signal-to-noise ratio, and stochastic resonance with a spatiotemporal input signal, characterized by the correlation function between the input and output signals, are observed for proper coupling between elements.

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