Stochastic Resonance Effect Research Articles

Noise as a Factor of Useful Signal Amplification Based on the Effect of Stochastic Resonance

Abstract The effect of stochastic resonance is investigated. The principles of the effect are considered on the basis of a Brownian particle moving in a system with a symmetric bistable potential. Different from the widely existing noise elimination methods, stochastic resonance enables a new method to utilize the energy of noises, nonlinear system, and signal frequency to reach certain weak signal enhancement effects that noise elimination cannot perform well. The presence of noise at the input of nonlinear systems possessing the effect of the stochastic resonance allows to stand out a weak signal from an additive mixture with white Gaussian noise. The equation and structural scheme of stochastic resonance are considered The conditions for the occurrence of stochastic resonance are formulated and the determining role of noise variance in the realization of this effect is shown. For the first time, a numerical calculation of standing out of harmonic oscillation from an additive mixture with white Gaussian noise based on the stochastic resonance effect is carried out. The output signal-to-noise ratio dependence of the stochastic resonator on the intensity of input noise and the input signal frequency is investigated. The frequency dependencies of the output signal are investigated and the components of this signal are analysed. It is shown that the stochastic resonator acts as a low-pass filter and reduces the output noise level. Numerical modelling of the stochastic resonance effect also shows that the output signal of the stochastic resonator contains odd harmonics of the input oscillation, which is characteristic of nonlinear systems. It is shown that the stochastic resonance effect can be widely used in radio engineering and telecommunications to amplify the useful signal.

Стохастический резонанс при определении оценки характеристической функции Ляпунова

The purpose of the paper is to investigate the phenomenon of stochastic resonance in a digital filter under the conditions of exposure to an additive mixture of a quasi-deterministic signal and a concentrated interference. The phenomenon of stochastic resonance in a digital filter based on the Lyapunov characteristic function is considered. In the process of modelling of the digital filter the effect and indices of stochastic resonance at filtering of additive mixture of quasi-deterministic signal and concentrated noise are established. The spectral characteristics of the output signal of the digital filter under the conditions of stochastic resonance occurrence are investigated. The results of modelling of a digital filter under the influence of an additive mixture of a useful signal and a concentrated noise are given. Modelling of the digital filter is carried out for cases when the frequency of the interference is equal to the frequency of the useful signal, the frequency of the interference is in the frequency band of the useful signal, as well as when the frequency of the interference is outside the frequency band of the useful signal. The presence of the phenomenon of stochastic resonance under the influence of concentrated interference is shown. The positive influence of the concentrated noise on the characteristics of the digital filter is shown. The improvement of signal/noise ratio at the output of the system in more than 180 times in comparison with the signal/noise ratio at its input is obtained. A comparison of the results of the study of the phenomenon of stochastic resonance in the case of the effects of concentrated noise and «white» noise is given.

Delayed-feedback oscillators replicate the dynamics of multiplex networks: Wavefront propagation and stochastic resonance

The widespread development and use of neural networks have significantly enriched a wide range of computer algorithms and promise higher speed at lower cost. However, the imitation of neural networks by means of modern computing substrates is highly inefficient, whereas physical realization of large scale networks remains challenging. Fortunately, delayed-feedback oscillators, being much easier to realize experimentally, represent promising candidates for the empirical implementation of neural networks and next generation computing architectures. In the current research, we demonstrate that coupled bistable delayed-feedback oscillators emulate a multilayer network, where one single-layer network is connected to another single-layer network through coupling between replica nodes, i.e. the multiplex network. We show that all the aspects of the multiplexing impact on wavefront propagation and stochastic resonance identified in multilayer networks of bistable oscillators are entirely reproduced in the dynamics of time-delay oscillators. In particular, varying the coupling strength allows suppressing and enhancing the effect of stochastic resonance, as well as controlling the speed and direction of both deterministic and stochastic wavefront propagation. All the considered effects are studied in numerical simulations and confirmed in physical experiments, showing an excellent correspondence and disclosing thereby the robustness of the observed phenomena.

Stochastic Resonance Effect in Segmented Underdamped Asymmetric Tristable System and Its Application in Weak Signal Detection Research

Stochastic Resonance Effect in Segmented Underdamped Asymmetric Tristable System and Its Application in Weak Signal Detection Research

Self-gating stochastic-resonance-based autoencoder for unsupervised learning.

Incorporating additive noise components to an ensemble of McCulloch-Pitts neurons can enhance the information representation of the input, asymptotically approaching the average firing probability for large enough ensembles. We further multiply the input by the average firing probability to control the higher probability of self-gating, thereby forming a unified noise-boosted activation model with learnable noise-related hyperparameters. This gating strategy plays a crucial role in improving the performance of neural networks, as evidenced by the optimization of the autoencoder loss at nonzero optimal-noise-scaling hyperparameters, a phenomenon termed self-gating stochastic resonance. Experiments with designed autoencoders using noise-boosted activation functions demonstrate the potential applications of the self-gating stochastic resonance effect in the field of unsupervised learning.

Haptic Sensation Enhancement via the Stochastic Resonance Effect and Its Application to Haptic Feedback for Myoelectric Prosthetic Hands

Haptic Sensation Enhancement via the Stochastic Resonance Effect and Its Application to Haptic Feedback for Myoelectric Prosthetic Hands

Moment dynamics for stochastic resonance in active rotator systems

We investigate the dynamics of active rotator systems by the moment closure method based on matching derivatives. This method is illustrated and verified in terms of three systems: the single-element rotator, the two coupled rotators and the mean field coupled rotators. Using the moment closure method, we study the effect of common noise on active rotator systems from the perspective of stochastic resonance. It is shown that the noise-induced stochastic resonance and parameter-induced stochastic resonance occur in the above three systems. Our observation discloses that the two kinds of stochastic resonance effect can be enhanced by both increasing coupling strength and the number of coupled rotators.

Two-finger Stiffness Discrimination with the Stochastic Resonance Effect

We investigated the ability of two fingers to discriminate stiffness with stochastic resonance. It is known that the haptic perception at the fingertip improves when vibrotactile noise propagates to the fingertip, which is a phenomenon called the stochastic resonance. The improvement in the haptic sensation of a fingertip depends on the intensity of the noise propagating to the fingertip. An improvement in the haptic sensation of multiple fingertips does not require multiple noise sources, such as vibrators, to be attached to multiple fingertips; i.e., even a single vibrator can propagate noise to multiple fingers. In this study, we focus on stiffness discrimination as a task using multiple fingers, in which the thumb and index finger are used to touch an object and perceive its stiffness. Subsequently, we demonstrate that the stiffness perception is improved by propagating sufficiently intense noise to the thumb and index finger using only a single vibrator. The findings indicate the possibility of improving the haptic sensation at multiple fingertips using one vibrator.

Определение предела Шеннона с использованием особых свойств прикладной системы

The aim of the paper is to preserve the fundamental nature of the Shannon limit and constraints in the mathematical theory of communication and to find a compromise solution for changing the boundary of the signal-to-noise ratio, at which the probability of errors is minimized, by using the special properties of the applied system, i.e., the modulator and demodulator. In this case, the "ideality" of the applied system according to the Shannon definition is preserved and supplemented by special properties obtained in our time, from the application of the Lyapunov characteristic function and the action of the stochastic resonance effect discovered at the end of the 20th century. Applied system one and applied system two are considered using the results of previous research and the special properties of the systems are identified. The applied systems are adapted to demodulators of signals with varying Lyapunov characteristic function. A new bound on the fundamental Shannon limit is computed. Taking into account the properties of the system, it is proposed to correct the Shannon limit to the value of −17.7 dB when transmitting messages with low error probability.

Frequency modulated signal standing out by stochastic resonance effect

In this paper, the phenomenon which is known as stochastic resonance is considered to the signal processing application. Signal standing out with the presence of noise is considered to be one of the basic problems of telecommunication and radioengineering. The stochastic resonance effect is shown to provide significant improvement of some characteristics of the information signal, such as power gain, and noise dispersion at the system output at a certain optimal noise level. In the present article, Minimum Shift Keying signal mixed with Gaussian white noise has been studied using stochastic resonance effect. Noise coefficient, which is one of the quantitative characteristics of noise immunity is calculated and investigated.

Autoregression, First Order Phase Transition, and Stochastic Resonance: A Comparison of Three Models for Forest Insect Outbreaks

Three models of abundance dynamics for forest insects that depict the development of outbreak populations were analyzed. We studied populations of the Siberian silkmoth Dendrolimus sibiricus Tschetv. in Siberia and the Far East of Russia, as well as a population of the pine looper Bupalus piniarius L. in Thuringia, Germany. The first model (autoregression) characterizes the mechanism where current population density is dependent on population densities in previous k years. The second model considers an outbreak as analogous to a first-order phase transition in physical systems and characterizes the outbreak as a transition through a potential barrier from a low-density state to a high-density state. The third model treats an outbreak as an effect of stochastic resonance influenced by a cyclical factor such as solar activity and the “noise” of weather parameters. The discussion focuses on the prediction effectiveness of abundance dynamics and outbreak development for each model.

Зависимость стохастического резонанса в нелинейной системе от характеристик каждого слагаемого аддитивной смеси

A nonlinear system was investigated using a modeling approach, constructed based on the scheme of a digital filter using the Lyapunov characteristic function. The phenomenon of stochastic resonance was observed in the nonlinear system when there was an additive mixture of a quasi-deterministic signal and noise at the system input. Stochastic resonance improves the signal-to-noise ratio at the system output by more than 15400 times compared to its value at the system input. The recorded number may vary and represents the main characteristic of the resonance. The dependence of the stochastic resonance characteristic on the variations of the probabilistic characteristics of the quasi-deterministic signal and noise was studied. An analysis of experimental data describing the values of the characteristic and the peculiarities of the stochastic resonance effect in the nonlinear system was performed. Additionally, a connection between the value of the resonance characteristic and the total energy of the periodic signal was discovered for the first time.

Зависимость стохастического резонанса в нелинейной системе от характеристик каждого слагаемого аддитивной смеси

A nonlinear system was investigated using a modeling approach, constructed based on the scheme of a digital filter using the Lyapunov characteristic function. The phenomenon of stochastic resonance was observed in the nonlinear system when there was an additive mixture of a quasi-deterministic signal and noise at the system input. Stochastic resonance improves the signal-to-noise ratio at the system output by more than 15400 times compared to its value at the system input. The recorded number may vary and represents the main characteristic of the resonance. The dependence of the stochastic resonance characteristic on the variations of the probabilistic characteristics of the quasi-deterministic signal and noise was studied. An analysis of experimental data describing the values of the characteristic and the peculiarities of the stochastic resonance effect in the nonlinear system was performed. Additionally, a connection between the value of the resonance characteristic and the total energy of the periodic signal was discovered for the first time.

Logistic stochastic resonance in the Hodgkin–Huxley neuronal system under electromagnetic induction

Hodgkin–Huxley neurons can be used as logic gates to perform reliable logic operations under an optimal noise intensity window. Fluctuations in ion concentrations inside and outside the neuron cell generate time-varying electromagnetic fields regulating neuronal dynamics. In this paper, a modified Hodgkin–Huxley neuron model is used to report the phenomenon of logical stochastic resonance under electromagnetic effects. The results show that electromagnetic induction affects the speed of neuronal response when switching to logic signals. Appropriately reducing the magnitude of the external bias current allows Hodgkin–Huxley neurons to perform reliable logic operations while consuming less energy. However, regulating the signal strength requires a trade-off between the reliability of logic operations and energy consumption. We further extend the logical stochastic resonance effect to neuronal networks. It is found that an appropriate increase in coupling strength has a favorable impact on system logic operations. The dynamical mechanism is explained in terms of bifurcation diagrams and phase space. Finally, we also compare the difference in the reliability of logical operations between small-world and scale-free networks. Small-world networks outperform scale-free networks for logical operations. Our results contribute to the study of neuronal simulation circuits with logic computation functions, and provides important clues for building new neuron-based logic devices with high energy efficiency.

An image denoising method based on the nonlinear Schrödinger equation and spectral subband decomposition

Most denoising methods inevitably smooth the image while denoising, which makes it difficult to effectively maintain the structural information and detail information of the original noise-free image. Stochastic resonance can directly convert the noise energy into signal energy, and denoising by stochastic resonance retains the signal energy. Therefore, this paper presents an image denoising method based on the nonlinear Schrödinger equation. First, by analyzing the dynamic stochastic resonance effect in a nonlinear optical system, the nonlinear Schrödinger equation is derived to describe the signal propagation in the system, and the equation is extended to construct a two-dimensional image denoising model. Then, we propose an image denoising algorithm based on image spectral subband decomposition. The algorithm decomposes the image spectrum into different frequency domain subbands and uses the Schrödinger denoising model to denoise the high-frequency subbands containing the rich structure and detailed information of the image. A series of comparative experiments show that the proposed method can significantly improve the image signal-to-noise ratio while effectively restoring image details and has better performance than other typical methods in the case of high-intensity noise.

Chimera resonance in networks of chaotic maps.

We explore numerically the impact of additive Gaussian noise on the spatiotemporal dynamics of ring networks of nonlocally coupled chaotic maps. The local dynamics of network nodes is described by the logistic map, the Ricker map, and the Henon map. 2D distributions of the probability of observing chimera states are constructed in terms of the coupling strength and the noise intensity and for several choices of the local dynamics parameters. It is shown that the coupling strength range can be the widest at a certain optimum noise level at which chimera states are observed with a high probability for a large number of different realizations of randomly distributed initial conditions and noise sources. This phenomenon demonstrates a constructive role of noise in analogy with the effects of stochastic and coherence resonance and may be referred to as chimera resonance.

Enhancing Performance of Convolutional Neural Network-Based Epileptic Electroencephalogram Diagnosis by Asymmetric Stochastic Resonance.

Epilepsy is a chronic disorder that leads to transient neurological dysfunction and is clinically diagnosed primarily by electroencephalography. Several intelligent systems have been proposed to automatically detect seizures, among which deep convolutional neural networks (CNNs) have shown better performance than traditional machine-learning algorithms. Owing to artifacts and noise, the raw electroencephalogram (EEG) must be preprocessed to improve the signal-to-noise ratio prior to being fed into the CNN classifier. However, because of the spectrum overlapping of uncontrollable noise with EEG, traditional filters cause information loss in EEG; thus, the potential of classifiers cannot be fully exploited. In this study, we propose a stochastic resonance-effect-based EEG preprocessing module composed of three asymmetrical overdamped bistable systems in parallel. By setting different asymmetries for the three parallel units, the inherent noise can be transferred to the different spectral components of the EEG through the asymmetric stochastic resonance effect. In this process, the proposed preprocessing module not only avoids the loss of information of EEG but also provides a CNN with high-quality EEG of diversified frequency information to enhance its performance. By combining the proposed preprocessing module with a residual neural network, we developed an intelligent diagnostic system for predicting seizure onset. The developed system achieved an average sensitivity of 98.96% on the CHB-MIT dataset and 95.45% on the Siena dataset, with a false prediction rate of 0.048/h and 0.033/h, respectively. In addition, a comparative analysis demonstrated the superiority of the developed diagnostic system with the proposed preprocessing module over other existing methods.

Image denoising using adaptive bi-dimensional stochastic resonance system

Using stochastic resonance (SR) mechanism, the output signal can be enhanced by adding noise to the nonlinear system. Therefore, an image denoising algorithm based on adaptive bi-dimensional stochastic resonance (ABSR) is proposed in this paper. Firstly, the image is sampled as a bi-dimensional signal, and an adaptive bi-dimensional dynamic nonlinear system model is constructed. The peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) of the output image are used as the double evaluation model of the adaptive system, and the optimal parameters of the model are automatically obtained by adjusting the parameters of the dynamic nonlinear system using the reverse positioning method. Compared with the traditional mean filter, median filter and one-dimensional stochastic resonance, the image restoration effect of dynamic adaptive bi-dimensional stochastic resonance is more closer to the original image, and the histogram, PSNR and SSIM of the output image are also significantly better than the other three methods. The results show that dynamic adaptive bi-dimensional stochastic resonance has better denoising effect and better robustness to the change of noise intensity in image processing.

Стохастический резонанс в цифровом фильтре на основе характеристической функции Ляпунова

The phenomenon of stochastic resonance in a radio engineering system, similar in structure to a digital filter based on the Lyapunov characteristic function, is considered. The physical meaning of stochastic resonance is revealed and the hypothesis of its existence in a radio engineering system is confirmed. In the process of modeling a digital filter, the effect and indicators of stochastic resonance were established when filtering an additive mixture of a quasi-deterministic signal and "white" noise. An improvement in the signal-to-noise ratio at the output of the system by a factor of 634 compared to the signal-to-noise ratio at its input was obtained when filtering an additive mixture of a centered quasi-deterministic signal and "white" noise. When filtering an additive mixture of a non-centered quasi-deterministic signal and "white" noise, the indicated stochastic resonance index is lower and amounts to 174 times. It is proposed to consolidate the phenomenon of stochastic resonance for a radio engineering system with such new definitions as the band and bandwidth of the resonance. Noise immunity increases noticeably in the resonance band in a digital modem with a circuit similar to a digital filter based on the Lyapunov characteristic function. The purpose of this work is to present a hypothesis with a future perspective, revealing the possibility of using a new effect in the construction of radio engineering systems.

EEG Analysis for Images Encode and Retrieval under White Noise Stimulation

Utilization of an EEG machine aids researchers in detecting the brain responses and states during provided stimulation. The EEG comes with multiple electrode channels for recording the electrical activity of the brain. This work aims to discover the brain responses under stimulation of white noise during images encoding and retrieving using the EEG machine. The motivation of this research is because limited previous works determine the association between memory encoding and retrieving process based on EEG analysis. Twenty college students participated in this experimental work. They were required to remember the images in two different conditions: control/silent and exposure to white noise with two task difficulties: easy and difficult phases. The EEG was recorded during the remembering and recalling period for data acquisition. The obtained raw EEG dataset was imported to .txt format for further processing. The Butterworth bandpass filter with a frequency range of 4 to 45 Hz was applied to filter the low and high noise components in the EEG signal. Next, the mean of de-noise EEG voltage was obtained to select the most affected channels. It was found that the Fp1, Fp2, F7, and F3 channels achieved the highest mean voltage that higher than 5 μV. Therefore, these channels were selected for extraction of relative rhythm power to investigate the effect of white noise on memory performance. The findings showed that the alpha, gamma, beta, and theta activities were highly found during the encoding and retrieving process when participants were exposed to white noise. These brain rhythms were related to participants' attentional level, information processing and calm state during the assessment. The behavioral data showed that the participants successfully remembered the images more when exposed to white noise compared to the control condition with percentage differences of 21% and 33% for easy and difficult phases due to the stochastic resonance effect and activation of brain rhythms.