Noise Induced Order: Stochastic Resonance

1998 ◽  
Vol 08 (05) ◽  
pp. 869-879 ◽  
Author(s):  
Lutz Schimansky-Geier ◽  
Jan A. Freund ◽  
Alexander B. Neiman ◽  
Boris Shulgin
Keyword(s):  
Information Theory ◽  
Stochastic Resonance ◽  
Noise Intensity ◽  
Electronic Circuit ◽  
Schmitt Trigger ◽  
Periodic Component ◽  
Large Signal ◽  
Input Signals

We investigate stochastic resonance in the framework of information theory. Input signals are taken from an electronic circuit and output signals are produced by a Schmitt trigger. These electronic signals are analyzed with respect to their informational contents. Conditional entropies and Kullback measures exhibit extrema for values of noise intensity in the range of stochastic resonance. However, it has to be noted that these extrema are related to synchronization effects, observed in stochastic resonance for large signal amplitudes, rather than to a peak in the related spectrum indicating some periodic component.

SUPPRESSION OF JAMMING IN EXCITABLE SYSTEMS BY APERIODIC STOCHASTIC RESONANCE

2004 ◽  
Vol 14 (10) ◽  
pp. 3519-3539 ◽  
Author(s):  
YING-CHENG LAI ◽  
ZONGHUA LIU ◽  
ARJE NACHMAN ◽  
LIQIANG ZHU
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Narrow Band ◽  
Broad Band ◽  
Effective Mechanism ◽  
Strong Broad Band ◽  
Chaotic Signals ◽  
Input Signals ◽  
Excitable Systems ◽  
Processing Information

To suppress undesirable noise (jamming) associated with signals is important for many applications. Here we explore the idea of jamming suppression with realistic, aperiodic signals by stochastic resonance. In particular, we consider weak amplitude-modulated (AM), frequency-modulated (FM), and chaotic signals with strong, broad-band or narrow-band jamming, and show that aperiodic stochastic resonance occurring in an array of excitable dynamical systems can be effective to counter jamming. We provide formulas for quantitative measures characterizing the resonance. As excitability is ubiquitous in biological systems, our work suggests that aperiodic stochastic resonance may be a universal and effective mechanism for reducing noise associated with input signals for transmitting and processing information.

Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Chunyan Bai ◽  
Luchun Du ◽  
Dongcheng Mei
Keyword(s):  
Stochastic Resonance ◽  
Growth Model ◽  
Noise Intensity ◽  
Critical Phenomenon ◽  
Fixed Ratio ◽  
Logistic Growth ◽  
Periodic Signal ◽  
Logistic Growth Model ◽  
Multiplicative Periodic Signal ◽  
Correlated Noises

AbstractThe stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

Stochastic Multiresonance in an Electronic Chaotic Circuit

2014 ◽  
Vol 24 (03) ◽  
pp. 1450027
Author(s):  
Thomas Stemler ◽  
Johannes P. Werner ◽  
Hartmut Benner
Keyword(s):  
Stochastic Resonance ◽  
Linear Response ◽  
Chaotic Dynamics ◽  
Chaotic Systems ◽  
Stochastic Systems ◽  
Electronic Circuit ◽  
Chaotic Circuit ◽  
Applied Method

Methods to estimate the amplification by stochastic resonance are tested in an electronic circuit experiment showing chaotic dynamics. We demonstrate that the linear response ansatz used for the estimation in stochastic systems can be also applied to chaotic systems showing crisis induced intermittency. In addition, the applied method explains the mechanism leading to stochastic multiresonance.

Parameter-Induced Stochastic Resonance in Wireless Sensor Network Signal Processing

2010 ◽  
Vol 121-122 ◽  
pp. 646-650
Author(s):  
Zi Kai Zhao ◽  
Guo Hua Hui
Keyword(s):  
Signal Processing ◽  
Wireless Sensor Network ◽  
Sensor Network ◽  
Stochastic Resonance ◽  
Noise Intensity ◽  
System Parameter ◽  
Wireless Sensor ◽  
Potential Well ◽  
Processing Level ◽  
Well Model

Parameter-induced stochastic resonance (PSR) using double potential well model was focused in this paper. Based on the former stochastic resonance study, system parameter µ was used to explore the resonance characteristics. A bluetooth-based wireless sensor network (WSN) was adopted to obtain the experimental data for parameter-induced stochastic resonance simulating. Under fixed noise intensity range, the changes of system parameter µ led to a systematic output resonance. Simulating results demonstrated that the systematic parameter µ could lead to stochastic resonance at signal processing level.

SIGNAL-TO-NOISE RATIO GAIN IN NON-DYNAMICAL AND DYNAMICAL BISTABLE STOCHASTIC RESONATORS

2002 ◽  
Vol 02 (03) ◽  
pp. L147-L155 ◽  
Author(s):  
PETER MAKRA ◽  
ZOLTAN GINGL ◽  
LASZLO B. KISH
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Schmitt Trigger ◽  
Total Power ◽  
Signal To Noise ◽  
Simulation Techniques ◽  
Duty Cycles ◽  
Signal Simulation ◽  
Noise Ratio ◽  
Snr Gain

It has recently been reported that in some systems showing stochastic resonance, the signal-to-noise ratio (SNR) at the output can significantly exceed that at the input; in other words, SNR gain is possible. We took two such systems, the non-dynamical Schmitt trigger and the dynamical double wellpotential, and using numerical and mixed-signal simulation techniques, we examined what SNR gains these systems can provide. In the non-linear response limit, we obtained SNR gains much greater than unity for both systems. In addition to the classical narrow-band SNR definition, we also measured the ratio of the total power of the signal to the power of the noise part, and it showed even better signal improvement. Here we present a brief review of our results, and scrutinise, for both the Schmitt-trigger and the double well potential, the behaviour of the SNR gain by stochastic resonance for different signal amplitudes and duty cycles. We also discuss the mechanism of providing gains greater than unity.

scholarly journals Stochastic Resonance in a Multistable System Driven by Gaussian Noise

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Peiming Shi ◽  
Pei Li ◽  
Shujun An ◽  
Dongying Han
Keyword(s):  
Stochastic Resonance ◽  
Gaussian Noise ◽  
Noise Intensity ◽  
Signal To Noise Ratio ◽  
Gaussian White Noise ◽  
State Theory ◽  
Elimination Theory ◽  
Resonance System ◽  
System Parameters ◽  
Nonmonotonic Function

Stochastic resonance (SR) is investigated in a multistable system driven by Gaussian white noise. Using adiabatic elimination theory and three-state theory, the signal-to-noise ratio (SNR) is derived. We find the effects of the noise intensity and the resonance system parametersb,c, anddon the SNR; the results show that SNR is a nonmonotonic function of the noise intensity; therefore, a multistable SR is found in this system, and the value of the peak changes with changing the system parameters.

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