scholarly journals Diagenetic Self-Organization and Stochastic Resonance in a Model of Limestone-Marl Sequences

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-18
Author(s):  
Ivan L’Heureux
Keyword(s):  
Stochastic Resonance ◽  
Reactive Transport ◽  
Transport Model ◽  
Nonlinear Dynamical Systems ◽  
Signal To Noise Ratio ◽  
Periodic Signal ◽  
Noise Strength ◽  
Nonlinear Dynamical ◽  
Milankovitch Cycle ◽  
Random Fluctuations

Banded patterns in limestone-marl sequences (“rhythmites”) form widespread sediments typical of shallow marine environments. They are characterized by alternations of limestone-rich layers and softer calcareous-clayey material (marl) extending over hundreds of meters with a thickness of a few tens of meters. The banded sequences are usually thought to result from systematic variations in the external environment, but the pattern may be distorted by diagenetic nonlinear processes. Here, we present a reactive-transport model for the formation of banded patterns in such a system. The model exhibits interesting features typical of nonlinear dynamical systems: (i) the existence of self-organized oscillating patterns between a calcite-rich mode (“limestone”) and a calcite-poor one (“marl”) for fixed environmental conditions and (ii) bistability between these two modes. We then illustrate the phenomena of stochastic resonance, whereby the multistable system is driven by a small external periodic signal (the 100,000 years’ Milankovitch cycle comes to mind) that is too weak to generate oscillations between the states on its own. In the presence of random fluctuations, however, the system generates transitions between the calcite-rich and calcite-poor states in statistical synchrony with the external forcing. The signal-to-noise ratio exhibits many maxima as the noise strength is varied. Hence, this amplification effect is maximized for specific values of the noise strength.

OPTIMAL TRANSITION RATE AND STOCHASTIC RESONANCE IN A BISTABLE SYSTEM DRIVEN BY POWER-LAW NOISE

2003 ◽  
Vol 14 (03) ◽  
pp. 303-310 ◽  
Author(s):  
J. F. L. FREITAS ◽  
M. L. LYRA
Keyword(s):  
Stochastic Resonance ◽  
Power Law ◽  
Transition Rate ◽  
Noise Intensity ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Resonance Phenomenon ◽  
Periodic Signal ◽  
Nonlinear Dynamical ◽  
Decay Exponent

In this work, we study the stochastic resonance phenomenon in a bistable nonlinear dynamical system in the presence of an uncorrelated noise source whose distribution decays asymptotically as P(ξ) ∝ 1/ξ2α. We investigate the influence of the decay exponent α on the transition rate and on the optimal noise intensity giving the maximum signal-to-noise ratio when a weak periodic signal is superposed to the external noise. We find that the transition rate achieves a maximum for a finite decay exponent α. However, the optimal noise intensity for stochastic resonance depicts a monotonic power-law correction relative to the usual behavior of nonlinear dynamical systems driven by Gaussian noises.

scholarly journals Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
F. Naha Nzoupe ◽  
Alain M. Dikandé
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Planck Equation ◽  
Relevant Information ◽  
Periodic Signal ◽  
Signal To Noise ◽  
Periodically Driven ◽  
Loop Area ◽  
Bistable Systems ◽  
Noise Ratio

AbstractThe occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker–Planck equation describing the system dynamics, together with the corresponding Ito–Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

Stochastic resonance in an array of integrate-and-fire neurons with threshold

2018 ◽  
Vol 32 (16) ◽  
pp. 1850169 ◽  
Author(s):  
Bingchang Zhou ◽  
Qianqian Qi
Keyword(s):  
Stochastic Resonance ◽  
Additive Noise ◽  
Signal To Noise Ratio ◽  
Array Size ◽  
Periodic Signal ◽  
Signal Parameter ◽  
Input Noise ◽  
Integrate And Fire ◽  
Noisy Input ◽  
Better Than

We investigate the phenomenon of stochastic resonance (SR) in parallel integrate-and-fire neuronal arrays with threshold driven by additive noise or signal-dependent noise (SDN) and a noisy input signal. SR occurs in this system. Whether the system is subject to the additive noise or SDN, the input noise [Formula: see text] weakens the performance of SR but the array size N and signal parameter [Formula: see text] promote the performance of SR. Signal parameter [Formula: see text] promotes the performance of SR for the additive noise, but the peak values of the output signal-to-noise ratio [Formula: see text] first decrease, then increase as [Formula: see text] increases for the SDN. Moreover, when [Formula: see text] tends to infinity, for the SDN, the curve of [Formula: see text] first increases and then decreases, however, for the additive noise, the curve of [Formula: see text] increases to reach a plain. By comparing system performance with the additive noise to one with SDN, we also find that the information transmission of a periodic signal with SDN is significantly better than one with the additive noise in limited array size N.

Stochastic resonance and stability for an ecological vegetation growth system driven by colored noises and multiplicative signal

2016 ◽  
Vol 30 (24) ◽  
pp. 1650308 ◽  
Author(s):  
Kang-Kang Wang ◽  
Ya-Jun Wang ◽  
Jian-Cheng Wu
Keyword(s):  
Stochastic Resonance ◽  
Multiplicative Noise ◽  
Signal To Noise Ratio ◽  
Periodic Signal ◽  
Expansion Process ◽  
Correlation Times ◽  
Vegetation Growth ◽  
Growth System ◽  
Speed Up ◽  
The Stability

In this paper, we investigate the steady-state properties and the transition rate for an ecological vegetation growth system induced by the terms of the colored multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can reduce the stability of the ecological system and slow down the development velocity of the vegetation, while two noise self-correlation times can increase the stability of the system and speed up the expansion process of the vegetation system. With respect to the stochastic resonance (SR) phenomenon caused by noise terms and a multiplicative weak periodic signal, the results show that the additive noise always enhances the SR effect, two noise self-correlation time terms can produce SR phenomenon, but play opposite roles in enhancing or inhibiting the SR effect under different parameter conditions. In particular, the two self-correlation times can keep up the maximum of the signal-to-noise ratio (SNR) invariant in specific situations. Analogously, the multiplicative noise can not only improve the SNR, but also restrain the SR phenomenon in different cases.

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.

Application of Stochastic Resonance in Digital Image Filtering

2012 ◽  
Vol 616-618 ◽  
pp. 2072-2075
Author(s):  
Yu Xin Zhang ◽  
Yu Liu ◽  
Hui Da Duan
Keyword(s):  
Stochastic Resonance ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Signal To Noise Ratio ◽  
Golden Section ◽  
Aerial Image ◽  
Maximum Point ◽  
Noise Strength ◽  
Resonance Theory ◽  
Filtering Algorithm

The principle, ideas, procedures and optimization problems of the filtering algorithm were presented in the article. First, the filtering algorithm procedures of aerial image based on stochastic resonance theory was introduced, then the curve of noise strength and peak signal to noise ratio (PSNR) was analyzed, a golden-section fast search algorithm was proposed and discussed as well to find out the maximum point of PSNR in the process of filtering. Experimental results indicate that the filtering method in this article is superior to other methods on high noise strength aerial image, and the stability and robustness are better than other methods . The multiples of filtering image’s PSNR is 1.2~1.4 times than other methods.

GLOBAL NONLINEAR NOISE REDUCTION USING RADIAL BASIS FUNCTIONS

1993 ◽  
Vol 03 (03) ◽  
pp. 589-596 ◽  
Author(s):  
JOACHIM HOLZFUSS ◽  
JAMES KADTKE
Keyword(s):  
Noise Reduction ◽  
Radial Basis Functions ◽  
Nonlinear Dynamical Systems ◽  
Signal To Noise Ratio ◽  
Chaotic Signal ◽  
Basis Functions ◽  
Nonlinear Dynamical ◽  
Radial Basis ◽  
Nonlinear Technique ◽  
Nonlinear Noise

A global nonlinear technique for noise reduction is described which is able to separate a noise source from a periodic or chaotic signal. The method is based on interpolation of the global flow of nonlinear dynamical systems with radial basis functions. Preliminary results indicate it provides a considerable increase of the signal-to-noise ratio. The algorithm is described in detail and numerical examples are given.

TEMPERATURE DEPENDENCE AND THE ROLE OF INTERNAL NOISE IN SIGNAL TRANSDUCTION EFFICIENCY OF CRAYFISH MECHANORECEPTORS

1995 ◽  
Vol 05 (01) ◽  
pp. 101-108 ◽  
Author(s):  
ELENI PANTAZELOU ◽  
CHRIS DAMES ◽  
FRANK MOSS ◽  
JOHN DOUGLASS ◽  
LON WILKENS
Keyword(s):  
Signal Transduction ◽  
Statistical Physics ◽  
Nonlinear Dynamical Systems ◽  
Internal Noise ◽  
Transduction Efficiency ◽  
Acclimation Temperature ◽  
Noisy Environment ◽  
Nonlinear Dynamical ◽  
Random Fluctuations

A simple phenomenon called stochastic resonance (SR), well known in nonlinear statistical physics, offers an explanation of how random fluctuations can enhance the detectability and/or the coherence of a weak signal in certain nonlinear dynamical systems. It is interesting to speculate that SR may play a role in the remarkable sensitivity exhibited by numerous biological sensory systems: systems which are themselves often inherently noisy and which, moreover, must usually operate in a noisy environment. A distinction is thus drawn between the external, or environmental, noise and the internal noise inherent in the sensory neurons themselves and distinguished by the randomness in time intervals between action potential spikes. We report the results of experiments with the internal noise, the intensity of which is varied by controlling the temperature of the preparation during the experiment. The useful range of temperatures could be extended by acclimating individual crayfish to a low or high temperature environment for many weeks prior to the experiment. Our results indicate that noise plays a significant role in signal transduction efficiency, increasing the signal-to-noise (SNR) ratio exponentially with noise intensity up to a maximum. Increasing the temperature beyond this maximum results in reduced SNRs and sharply reduced internal noise levels. The results of shifts in the data due to acclimation temperature can be removed by plotting the data versus the noise level, indicating that the noise may be a universal quantity in the dynamics of biological neurons.

STOCHASTIC RESONANCE AT THE ONSET OF FINITE- AMPLITUDE OSCILLATIONS IN SEMICONDUCTOR BREAKDOWN

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 1068-1074
Author(s):  
R. RICHTER ◽  
A. KITTEL ◽  
K. PYRAGAS ◽  
J. PARISI
Keyword(s):  
Low Temperature ◽  
Stochastic Resonance ◽  
Impact Ionization ◽  
Nonlinear Dynamical Systems ◽  
Random Perturbation ◽  
Finite Amplitude ◽  
Periodic Modulation ◽  
Nonlinear Dynamical ◽  
Temperature Impact ◽  
P Type

The phenomenon of stochastic resonance has been observed when looking at low-temperature impact ionization breakdown in p-type germanium crystals. Originally, such an effect was predicted for the class of bistable nonlinear dynamical systems which are subject to a periodic modulation as well as to random perturbation. We demonstrate first experimental evidence that stochastic resonance can also be detected in a monostable system, i.e., immediately below the onset of finite-amplitude oscillations during semiconductor breakdown.

Theory and method for weak signal detection in engineering practice based on stochastic resonance

2017 ◽  
Vol 31 (28) ◽  
pp. 1750212 ◽  
Author(s):  
Wenli Zhao ◽  
Linze Wang ◽  
Jian Fan
Keyword(s):  
Stochastic Resonance ◽  
Adiabatic Approximation ◽  
Signal To Noise Ratio ◽  
Energy Transition ◽  
Bistable System ◽  
Modulation Method ◽  
Engineering Practice ◽  
Periodic Signal ◽  
Frequency Components ◽  
Large Frequency

In this paper, the Kramers rate was derived using the Fokker–Planck (FP) equation with the condition of adiabatic approximation (the amplitude and frequency of signal detected are small [Formula: see text]) and the signal-to-noise ratio (SNR) was proved by means of Fourier transform and the power spectrum in bistable system. This is a concise and superior method to demonstrate the Kramers rate and SNR compared to the past methods. It is convenient for readers to understand. The SNR of the bistable system obtained shows that stochastic resonance (SR) can be used to realize energy transition from noise to a periodic signal under the adiabatic approximation condition. Therefore, SR could enhance the SNR of the output signal. The signal modulation technique was employed to transform the large frequency components into a small parameter signal to meet the adiabatic approximation requirement. Furthermore, we have designed the model of modulator. The simulation results show that the modulation method can generate SR in a bistable system and detect weak signals with large parameters from strong noise background.

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