Stochastic Resonance Phenomenon Research Articles

Overdamped Ising machine with stochastic resonance phenomena in large noise condition

Gain-dissipative Ising machines (GIMs) are dedicated devices that can rapidly solve combinatorial optimization problems. The noise intensity in traditional GIMs should be significantly smaller than its saturated fixed-point amplitude, indicating a lower noise margin. To overcome the existing limit, this work proposes an overdamped bistability-based GIM (OBGIM). Numerical test on uncoupled spin network show that the OBGIM has a different bifurcation dynamics from that of the traditional GIM. Moreover, the domain clustering dynamics on non-frustrated network proves that the overdamped bistability enables the GIM to suppress noise-induced random spin-state switching effectively; thus, it can function normally in an environment with a relatively large noise level. Besides, some prevalent frustrated graphs from the SuiteSparse Matrix Collection were adopted as MAXCUT benchmarks. The results show that the OBGIM can induce stochastic resonance phenomenon when solving difficult benchmarks. Compared with the traditional GIM, this characteristic makes the OBGIM achieve comparable solution accuracy in larger noise environment, thus achieving strong noise robustness.

Theoretical analysis and potential engineering application of an energy harvester

The technique of energy harvesting, which captures the energy from ambient vibrations, has received increasing attention due to its potential to power low-powered wireless sensors. Therefore, it is important to reveal the nonlinear dynamic mechanism to design a high-performance energy harvester. This paper describes an energy harvester with the decoupled bistable potential (DBEH), in which the potential function can be controlled independently by the barrier height or the barrier width. The harmonic balance method (HBM) is used to obtain the theoretical solutions, and the Jacobian matrix is provided to determine their stability. Thirdly, this paper thoroughly discusses the influence of barrier height and width on output responses and the multi-solution range. Finally, numerical simulations observe the stochastic resonance (SR) phenomenon and the inverse SR phenomenon of the DBEH with Gaussian white noise injection. The SR phenomenon of the DBEH is applied to bearing fault diagnosis, effectively enhancing fault characteristics.

Optimizing Work Extraction in the Presence of an Entropic Potential: An Entropic Stochastic Resonance.

We study the nontrivial thermodynamic responses of an overdamped Brownian system driven by an unbiased driving force when the particle is confined inside a bilobal irregular structure. The spatial irregularity of the confinement results in an effective entropic bistable potential along the direction of transport. We calculate the thermodynamic response functions in terms of the averaged work done and the absorbed heat over a cycle of driving. We find that the thermodynamic responses are influenced by the nonlinearity of the effective entropic potential, the frequency of the external periodic driving force, and the random thermal fluctuations in a nontrivial way. In the presence of an optimal amount of thermal noise and a favoring driving frequency, the process exhibits a resonance-like precedent in terms of both output work and absorbed heat. We explore the conditions to get best synchronized work extraction (or absorbed heat), which can be utilized as a potential quantifier of an entropic stochastic resonance phenomenon. Finally, we identify a hallmark of entropy dominance over an analogous energy-driven scenario in terms of output work.

Detection of principal and higher harmonic frequencies using stochastic resonance phenomenon in PBTTT-C14-based organic field-effect transistor

Stochastic resonance (SR) is an intriguing phenomenon in which noise, typically considered a detrimental aspect of electronic communication systems, assumes a beneficial role in the detection of undetectable signals. The SR phenomenon for detecting low-intensity optical signals using PBTTT-C14-based organic field-effect transistors (OFETs) is being reported. In this discourse, we explicate the sensing of an undetectable periodic optical signal with a frequency of 5 Hz, using a PBTTT-C14-based OFETs in the presence of a finite and optimal quantity of Gaussian noise (noise bandwidth of 1 Hz and noise amplitude of 2.0, 4.0, 6.0, and 7.5 V). The detection of higher harmonics for optical signals using the SR phenomenon has not been hitherto explored for OFETs. This report presents a noteworthy finding elucidating the detection of the principal frequency and also higher harmonics of the optical signal. This simplistic methodology for examining the SR phenomenon holds great promise in identifying its robust utility in diverse real-world contexts.

Анализ периодической компоненты выходного сигнала цифрового фильтра в условиях возникновения стохастического резонанса

The periodic component of the output signals of a digital filter based on the Lyapunov characteristic function under the influence of an additive mixture of signal and noise is studied. The possibility of using the level of the periodic component of the output signal to characterize the phenomenon of stochastic resonance in digital devices is shown. The levels of the periodic component of the output signals of a digital filter based on the Lyapunov characteristic function and a linear digital filter at different noise levels at the input are compared. The change of the level of the periodic component of the output signal depending on the noise intensity for these digital filters is shown. The results of using the periodic component of the output signal of a digital filter based on the Lyapunov characteristic function in solving the problem of signal detection on the background of noise are presented.

Collective dynamics of fluctuating–damping coupled oscillators in network structures: Stability, synchronism, and resonant behaviors

The investigation of collective behaviors and synergies in coupled systems holds great significance in many fields. In this paper, we propose the coupled system of overdamped fluctuating–damping oscillators in a general network framework. Our initial theoretical analysis focuses on the system’s synchronization and stability, revealing that both the first and second moments of the mean field are asymptotic stability, and the system exhibits a property of stochastic asymptotic synchronization with the mean field, irrespective of coupled structures. Furthermore, we explore the system’s collective behaviors by analyzing the output amplitude amplification (OAA), where we observe the emergence of generalized stochastic resonance (GSR) phenomena. Finally, we numerically verify the influence of system parameters on stability and synchronization in different coupled structures by introducing the mean first stability time and mean first synchronization time in the simulations. Our findings indicate that the structure does not significantly influence the system stability, whereas it does play a synergistic role in influencing the synchronization. Moreover, we further extend the investigation in complex networks, and observe the non-monotonous phenomena of mean first synchronization time varying with the heterogeneity.

Dynamic Properties for Time-Delayed Grazing Ecosystem Driven by Lévy Noise and Gaussian Noise

In this paper, we establish a stochastic dynamical grazing ecosystem with time delays and fluctuations. The effects of time delay, Gaussian noise and Lévy noise on the stationary probability distribution (SPD), the mean first passage time (MFPT) and stochastic resonance (SR) are analyzed. Our research results show the following: (i) For small time delay, the increasing Gaussian noise intensity leads to catastrophic regime shift (CRS) from high vegetation state to low vegetation state, while the increasing Lévy noise intensity contributes to the recovery of these shifts. For large time delay, the increasing Gaussian noise intensity or Lévy noise intensity causes the CRS phenomenon, the larger the time delay, the more frequent the CRS phenomenon. (ii) The increasing Gaussian noise intensity can diminish the stability of the high vegetation state and low vegetation state, the increasing Lévy noise intensity and Lévy stability index can enhance the stability of the high vegetation state and diminish the stability of the low vegetation state. The increasing Lévy noise intensity can lead to noise-enhanced stability (NES) of the high vegetation state, and the larger the time delay, the more pronounced the NES phenomenon. (iii) The increase of time delay can weaken SR phenomenon when signal-to-noise ratio (SNR) is a function of Gaussian noise intensity and Lévy noise intensity.

Rotational stochastic resonance in multistable systems

Stochastic resonance is a well-known phenomenon that intermediate amount of noise can enhance the signal-to-noise ratio of systems subjected to weak signals. Since the discovery of stochastic resonance, it has aroused tremendous attention during the past several decades due to its counterintuitive nature. Previous focus is mainly devoted to low-dimensional bistable systems with only one sinusoid-type weak signal. In this work, we extend the boundary of the traditional stochastic resonance by considering two-dimensional multistable systems driven by rotational sinusoid-type weak signals. We consider an artificial triple-well system and also a more realistic four-well system model. The rotational characteristics of noise-induced switching between stable wells (clockwise or anticlockwise) can be controlled by the signal frequency and the noise intensity, which is a markedly difference from the classical ones. Thus, we term it as rotational stochastic resonance. The rotational stochastic resonance phenomenon can be illustrated by the Penrose stairs and can be quantified by the proposed minimum potential coincidence index and the minimum potential locking index. The rotational stochastic resonance and its control investigated in this paper may shed some light on more complex resonance phenomena and experimental applications.

Statistical complexity and stochastic resonance of an underdamped bistable periodic potential system excited by Lévy noise

This paper focuses on the underdamped bistable potential system's stochastic resonance (SR) phenomenon under Lévy noise excitation. The statistical complexity of the system is analyzed under the changes of damping factor, amplitude and frequency of the periodic signal, stability index and skew parameter of Lévy noise, and the effects of the changes of above parameters on SR are investigated. The results show that the increase of the damping factor hinders the appearance of SR phenomenon; the larger amplitude and lower frequency of the periodic signal are beneficial to the appearance of SR; the larger stability index of the noise parameter, the more likely SR occurs, and the change of the skew parameter has little effect on the SR. Because the Bandt-Pompe (B-P) algorithm is used in the information-theoretic measure to model the statistical complexity of this system, the robustness of the method is analyzed by changing the embedding dimension and the length of residual time interval sequence in the B-P algorithm. Finally, the mean first passage time of the particle is calculated as a function of the noise intensity and the noise-enhanced stability effect is found.

The synchronization, stability and stochastic resonance of stochastic global coupled system

In this paper, we aim at a global coupled system influenced by a multiplicative dichotomous noise and an additive Gaussian white noise. Since the analysis of the synchronization and stability is important to a coupled system, and there is little general method to analyze them. We provide methods to derive the synchronization and stability of particles in the system. Guaranteed by the synchronization and stability, we obtain the analytic expression of each particle’s average displacement. To verify our results, we use stochastic Taylor expansion to derive numerical iterative expressions of the displacements of particles. As for numerical simulations, we find that the numerical solutions match the analytical solutions, and we display the synchronization speed of particles, the stable region of noise intensity, resonance areas and the output amplitude gain with respect to various parameters of the system. We find that the phenomenon of stochastic resonance occurs if and only if the parameters are situated in the resonance area.

The inverse stochastic resonance in a small-world neuronal network under electromagnetic stimulation

Electromagnetic stimulation is an important neuromodulation technique that modulates the electrical activity of neurons and affects cortical excitability for the purpose of modulating the nervous system. The phenomenon of inverse stochastic resonance is a response mechanism of the biological nervous system to external signals and plays an important role in the signal processing of the nervous system. In this paper, a small-world neural network with electrical synaptic connections was constructed, and the inverse stochastic resonance of the small-world neural network under electromagnetic stimulation was investigated by analyzing the dynamics of the neural network. The results showed that: the Levy channel noise under electromagnetic stimulation could cause the occurrence of inverse stochastic resonance in small-world neural networks; the characteristic index and location parameter of the noise had significant effects on the intensity and duration of the inverse stochastic resonance in neural networks; the larger the probability of randomly adding edges and the number of nearest neighbor nodes in small-world networks, the more favorable the anti-stochastic resonance was; by adjusting the electromagnetic stimulation parameters, a dual regulation of the inverse stochastic resonance of the neural network can be achieved. The results of this study provide some theoretical support for exploring the regulation mechanism of electromagnetic nerve stimulation technology and the signal processing mechanism of nervous system.

Impact of Non-Gaussian Noise and Time Delay on Stability and Stochastic Resonance for a FitzHugh-Nagumo Neural System Subjected to a Multiplicative Periodic Signal

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times [Formula: see text] and [Formula: see text] can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay [Formula: see text] and the correlation time [Formula: see text] of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time [Formula: see text] of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

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.

Entropic stochastic resonance for a confined system driven by two constant forces and multiplicative noise

The entropic stochastic resonance (ESR) phenomenon for a confined system driven by two constant forces, by two periodic forces and multiplicative noise is studied. The Fokker-Planck equation corresponding to the confined structure is obtianed applying Fick-Jacob approximation. The transition rates from the stable states are derived under the adiabatic approximation condition. The signal-to-noise ratios (SNRs) for the fundamental and higher harmonics are derived by virtue of two-state theory. Analysis result indicates that the SNR for fundamental harmonic decreases as increasing the constant force along x-direction, while the SNR for fundamental harmonic can obtain one maxmimum value with the increment of the constant force along y-direction. Each of the SNRs for higher harmonics can get one resonance peak as increasing the two constant forces. Two peaks appear when the SNRs vary with the multiplicative noise intensity, while only one peak value takes place when the SNRs change with the additive noise strength. The influence of the boundary parameters of the confined system on the SNRs is discussed.

Impact of Double Time Delays on Regime Shift and Stochastic Resonance for a Species Population System Driven by Colored Correlated Multiplicative and Additive Noises

In this paper, the characteristics for the state transition between the boom state and the extinction one, varius stochastic resonance (SR) phenomena for a species population system induced by double time delays and colored cross-correlated Gaussian noises are investigated. The control of the species population system has an important effect on ecological balance and the development of human living environment. By means of the numerical calculation of the mean extinction time and the stationary probability density function (SPDF), we can figure out some fact: both external and internal noises, the noise correlation strength and its correlation time, one time delay can all reduce the ecological stability and shorten the survival time of the system; while the other time delay can enhance significantly the biological stability and postpone the extinction of the population. For the mean extinction time (MET) of the species population, it is found that noise correlation strength, time delay, the noise correlation time can all reduce the peak value of the MET, which leads to the reduction of the life cycle. Inversely, the other time delay will not change the maximum of the MET, and induce the peak value to shift to the left. With respect to the SNR, it is discovered that in the noise correlation strength and its correlation time, one-time delay mainly plays a prominent role in inhibiting the SR effect. On the contrary, the multiplicative noise can result in the enhancement of the resonant peak. In particular, the other time delay and the additive noise can stimulate the SR effect for the SNR during the initial period. However, the further increase of them will bring about the reduction of the resonant phenomenon.

Optimal transport of active particles induced by substrate concentration oscillations.

We show the existence of a stochastic resonant regime in the transport of active colloidal particles under confinement. The periodic addition of substrate to the system causes the spectral amplification to exhibit a maximum for an optimal noise level value. The consequence of this is that particles can travel longer distances with lower fuel consumption. The stochastic resonance phenomenon found allows the identification of optimal scenarios for the transport of active particles, enabling them to reach regions that are otherwise difficult to access, and may therefore find applications in transport in cell membranes and tissues for medical treatments and soil remediation.

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.

Modulation of Visual Contrast Sensitivity with tRNS across the Visual System, Evidence from Stimulation and Simulation

Transcranial random noise stimulation (tRNS) has been shown to significantly improve visual perception. Previous studies demonstrated that tRNS delivered over cortical areas acutely enhances visual contrast detection of weak stimuli. However, it is currently unknown whether tRNS-induced signal enhancement could be achieved within different neural substrates along the retino-cortical pathway.In 3 experimental sessions, we tested whether tRNS applied to the primary visual cortex(V1) and/or to the retina improves visual contrast detection. We first measured visual contrast detection threshold (VCT; N=24, 16females) during tRNS delivery separately over V1 and over the retina, determined the optimal tRNS intensities for each individual(ind-tRNS), and retested the effects of ind-tRNS within the sessions. We further investigated whether we could reproduce the ind-tRNS-induced modulation on a different session (N=19, 14females). Finally, we tested whether the simultaneous application of ind-tRNS to the retina and V1 causes additive effects. Moreover, we present detailed simulations of the induced electric field across the visual system.We found that at the group level tRNS decreases VCT compared to baseline when delivered to the V1. Beneficial effects of ind-tRNS could be replicated when retested within the same experimental session but not when retested in a separate session. Applying tRNS to the retina did not cause a systematic reduction of VCT, irrespective of whether the individually optimized intensity was considered or not. We also did not observe consistent additive effects of V1 and retina stimulation.Our findings demonstrate significant tRNS-induced modulation of visual contrast processing in V1, but not in the retina.Significance statementOur findings confirm previous evidence showing acute online benefits of tRNS of V1 on visual contrast detection in accordance with the stochastic resonance phenomenon. We further extend it, demonstrating that the optimal tRNS intensity varies among participants, but when individually tailored it can improve visual processing when re-tested within the experimental session. The tRNS-induced enhancement in visual sensitivity was observed for cortical contrast processing, but stimulation of the retina did not lead to systematic effects.