Stochastic Resonance Phenomenon Research Articles

Behavioural stochastic resonance across the lifespan.

Stochastic resonance (SR) is the phenomenon wherein the introduction of a suitable level of noise enhances the detection of subthreshold signalsin non linear systems. It manifests across various physical and biological systems, including the human brain. Psychophysical experiments have confirmed the behavioural impact of stochastic resonance on auditory, somatic, and visual perception. Aging renders the brain more susceptible to noise, possibly causing differences in the SR phenomenon between young and elderly individuals. This study investigates the impact of noise on motion detection accuracy throughout the lifespan, with 214 participants ranging in age from 18 to 82. Our objective was to determine the optimal noise level to induce an SR-like response in both young and old populations. Consistent with existing literature, our findings reveal a diminishing advantage with age, indicating that the efficacy of noise addition progressively diminishes. Additionally, as individuals age, peak performance is achieved with lower levels of noise. This study provides the first insight into how SR changes across the lifespan of healthy adults and establishes a foundation for understanding the pathological alterations in perceptual processes associated with aging.

Potential of coupled array harvester in enhanced energy harvesting.

Harvesting energy from nonlinear systems has been at the centre of research in the energy harvesting community. Many such proposed systems are single nonlinear harvester. While these systems show an increase in bandwidth of harvesting frequency, overall, they are not effective enough in power generation. This article studies power harvesting and frequency bandwidth characteristics of an array of harvesters. Multiple harvesters are considered with linear and nonlinear coupling between the harvesters. The phenomena of internal resonance (IR) and stochastic resonance (SR) are reported. The IR in multiple coupled nonlinear harvesters is explored using multiple-scale analysis. A parametric study is conducted to demonstrate the effect of coupling strength, frequency mistuning, innate nonlinearity and other parameters. The parametric study helped establish effective ways to increase bandwidth. Moreover, a stochastically loaded linearly coupled bistable harvester array is numerically analysed to find the effect of coupling strength and array size on the phenomenon of SR and on the system's harvesting performance. Through these studies, the potential of multiple coupled nonlinear harvesters in enhanced energy harvesting is demonstrated under both harmonic and stochastic excitation.This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Optimizing power-efficiency dynamics in ambient energy harvesting: Exploring trade-offs, linearity, and synergy

As the demand for low-power electronics and IoT devices grows, ambient energy harvesting appears to be a promising alternative for powering such systems in the long run. However, optimizing power and efficiency concurrently in such systems is challenging, involving balancing a number of variables. This paper investigates the optimization of power and efficiency in ambient energy harvesting systems focusing on nonlinear oscillator electromechanical harvesters subjected to multiplicative time-correlated ambient noise. Through extensive numerical simulations, we reveal distinct relationships between power and efficiency, influenced by various parameters. We observe autonomous stochastic resonance phenomena, elucidating a linear power-efficiency trend for small noise correlation time under fixed noise variance but limiting simultaneous power and efficiency optimization beyond a threshold. Under fixed noise strength, there is a trade-off between power and efficiency. Additionally, damping strength, piezoelectric parameters, and capacitor charging time impact power and efficiency linearly. These insights enhance understanding of power efficiency dynamics in ambient energy harvesting, thereby offering practical recommendations for parameter selection to maximize both power output and efficiency in the next generation of electronics.

Coupled piecewise tri-stable stochastic resonance system driven by dual inputs and joint EMD/VMD analysis

A novel piecewise tri-stable stochastic resonance (NPTSR) system is proposed to address the issue of output saturation caused by high-order terms limitation in this paper. Building upon this, the exploration is extended to a coupled piecewise tri-stable stochastic resonance system driven by dual inputs (DCPTSR). First, we uncover the influence of dual input interaction on output quality, finding that when the fRequencies of the two input signals are consistent, varying the amplitude of the driving signal can effectively enhance the output performance of the target signal. Secondly, by utilizing the adiabatic approximation theory, the steady-state probability density (SPD) and signal-to-noise ratio (SNR) of the DCPTSR system are derived, which allows us to analyze the effects of various parameters on both SPD and SNR. Next, three combined denoising systems, namely EMD-DCPTSR, VMD-DCPTSR, and SDCPTSR, are constructed by utilizing empirical mode decomposition (EMD), variational mode decomposition (VMD), and the stochastic resonance (SR). Through numerical simulations, we demonstrate that the combined denoising system outperforms the stand-alone SR system, and we analyze the stochastic resonance phenomenon of the DCPTSR system using the spectral amplification (SA) coefficient as an evaluation index. Finally, to assess practical applicability, these systems are deployed for bearing fault detection. The experimental results exhibit notable signal-to-noise gain improvements for the DCPTSR system compared to standalone SR systems by 0.7699 ∼ 9.4541 dB. The EMD-DCPTSR system shows signal-to-noise gain improvements of 0.3245 ∼ 1.1709 dB compared to the VMD-DCPTSR and SDCPTSR systems. Moreover, all three combined denoising systems outperform the standalone SR system in terms of signal processing capabilities. In conclusion, this paper extensively investigates the interaction between the two input signals in a dual-input system and studies the output performance of using EMD, VMD, and SR as preprocessing methods for the SR system. Through numerical simulations and practical engineering applications, we highlight the substantial advantages of combined denoising systems. These findings offer essential theoretical insights and promising prospects for engineering applications.

Efficient approximation of stochastic turning process based on power spectral density

Turning is one of the most important material removal processes in manufacturing, where the proper understanding of the process is crucial for the quality of the final product. In this study, the stochastic cutting force is utilized to enhance the existing 1-degree-of-freedom turning model. A stochastic model is adopted to address the stochastic resonance phenomenon occurring near stability boundaries. Additionally, a novel simplified stochastic model is introduced with additive noise only. The comparison of the two models reveals that, with the recommended noise intensity of 0.1 to 1%, there is no significant difference in the stability charts and mean square characteristics between the two models. As a result, the time-consuming numerical methods can be bypassed, as the simplified model offers a computationally more efficient analytical approach to compute variance based on power spectral density (PSD). By combining techniques such as D-separation to determine stability boundaries and the PSD-based variance calculation, it only takes a minute instead of hours to construct a heatmap using the introduced simplified stochastic turning model that clearly outlines dangerous stochastic resonance regions inside the stable domain.

Optimal navigability of weighted human brain connectomes in physical space

Communication protocols in the brain connectome describe how to transfer information from one region to another. Typically, these protocols hinge on either the spatial distances between brain regions or the intensity of their connections. Yet, none of them combine both factors to achieve optimal efficiency. Here, we introduce a continuous spectrum of decentralized routing strategies that integrates link weights and the spatial embedding of connectomes to route signal transmission. We implemented the protocols on connectomes from individuals in two cohorts and on group-representative connectomes designed to capture weighted connectivity properties. We identified an intermediate domain of routing strategies, a sweet spot, where navigation achieves maximum communication efficiency at low transmission cost. This phenomenon is robust and independent of the particular configuration of weights. Our findings suggest an interplay between the intensity of neural connections and their topology and geometry that amplifies communicability, where weights play the role of noise in a stochastic resonance phenomenon. Such enhancement may support more effective responses to external and internal stimuli, underscoring the intricate diversity of brain functions.

Dynamic properties of rumor propagation model induced by Lévy noise on social networks

Abstract Social networks are inevitably subject to disruptions from the physical world, such as sudden internet outages that sever local connections and impede information flow. While Gaussian white noise, commonly used to simulate stochastic disruptions, only fluctuates within a narrow range around its mean and fails to capture large-scale variations, Lévy noise can effectively compensate for this limitation. Therefore, a susceptible–infected–removed rumor propagation model with Lévy noise is constructed on homogeneous and heterogeneous networks, respectively. Then, the existence of a global positive solution and the asymptotic path-wise of the solution are derived on heterogeneous networks, and the sufficient conditions of rumor extinction and persistence are investigated. Subsequently, theoretical results are verified through numerical calculations and the sensitivity analysis related to the threshold is conducted on the model parameters. Through simulation experiments on Watts–Strogatz (WS) and Barabási–Albert networks, it is found that the addition of noise can inhibit the spread of rumors, resulting in a stochastic resonance phenomenon, and the optimal noise intensity is obtained on the WS network. The validity of the model is verified on three real datasets by particle swarm optimization algorithm.

Simple model to incorporate statistical noise based on a modified hodgkin-huxley approach for external electrical field driven neural responses

Noise activity is known to affect neural networks, enhance the system response to weak external signals, and lead to stochastic resonance phenomenon that can effectively amplify signals in nonlinear systems. In most treatments, channel noise has been modeled based on multi-state Markov descriptions or the use stochastic differential equation models. Here we probe a computationally simple approach based on a minor modification of the traditional Hodgkin-Huxley approach to embed noise in neural response. Results obtained from numerous simulations with different excitation frequencies and noise amplitudes for the action potential firing show very good agreement with output obtained from well-established models. Furthermore, results from the Mann–Whitney U Test reveal a statistically insignificant difference. The distribution of the time interval between successive potential spikes obtained from this simple approach compared very well with the results of complicated Fox and Lu type methods at much reduced computational cost. This present method could also possibly be applied to the analysis of spatial variations and/or differences in characteristics of random incident electromagnetic signals.

Multiple stochastic and inverse stochastic resonances with transition phenomena in complex corporate financial systems.

This study examines the role of periodic information, the mechanism of influence, stochastic resonance, and its controllable analysis in complex corporate financial systems. A stochastic predator-prey complex corporate financial system model driven by periodic information is proposed. Additionally, we introduce signal power amplification to quantify the stochastic resonance phenomenon and develop a method for analyzing stochastic resonance in financial predator-prey dynamics within complex corporate financial systems. We optimize a simplified integral calculation method to enhance the proposed model's performance, which demonstrates superiority over benchmark models based on empirical evidence. Based on stochastic simulations and numerical calculations, we can observe multiple stochastic and multiple inverse stochastic resonances. Furthermore, variations in initial financial information, periodic information frequency, and corporate growth capacity induced stochastic resonance and inverse stochastic resonance. These variations also led to state transitions between the two resonance behaviors, indicating transition phenomena. These findings suggest the potential for regulating and controlling stochastic and inverse stochastic resonance in complex corporate finance, enabling controllable stochastic resonance behaviors.

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.

Intrinsic mechanism of influence of channel blocking and noise on response state of multicompartmental neurons

The fine structure of multi-compartment neurons can simultaneously capture both temporal and spatial characteristics, offering rich responses and intrinsic mechanisms. However, current studies of the effects of channel blockage and noise on neuronal response states are mainly limited to single-compartment neurons. This study introduces an analytical method to explore theintrinsic mechanism of channel blockage and noise effects on the response states of multi-compartment neurons, by using the smooth Pinsky-Rinzel two-compartment neuron model as a case study. Potassium, sodium, and calcium ion channel blockage coefficient are separately introduced to develop a smooth Pinsky-Rinzel neuron model with ion channel blockage. Methods such as single-parameter bifurcation analysis, double-parameter bifurcation analysis, coefficient of variation, and frequency characteristics analysis are utilized to examine the effects of various ion channel blockages on neuronal response states. Additionally, smooth Pinsky-Rinzel neuron Subunit noise model and conductance noise model are constructed to investigate their response characteristics by using interspike interval analysis and coefficient of variation indicators. Subthreshold stimulation is used to explore the presence of stochastic resonance phenomena. Single-parameter bifurcation analysis of the ion channel blockage model elucidates the dynamic processes of two torus bifurcations and limit point bifurcations in Pinsky-Rinzel neuron firing under potassium ion blocking. Double-parameter bifurcation analysis reveals a nearly linear increase in the Hopf bifurcation node of potassium ions with input current, whereas sodium ions exhibit a two-stage pattern of linear decline followed by exponential rise. The analysis of average firing frequency and coefficient of variation indicates that the moderate potassium channel blockage promotes firing, sodium channel blockage inhibits firing, and calcium channel blockage shows the complex characteristics but mainly promotes firing. Subthreshold stimulation of the channel noise model demonstrates the stochastic resonance phenomena in both models, accompanied by more intense chaotic firing, highlighting the positive role of noise in neural signal transmission. The interspike interval and coefficient of variation indicators show consistent variation levels for both noise models, with the conductance model displaying greater sensitivity to membrane area and stronger encoding capabilities. This study analyzes the general frequency characteristics of potassium and sodium ions in a multi-compartment neuron model through ion channel blocking model, providing special insights into the unique role of calcium ions. Further, the study explores stochastic resonance by using ion channel noise model, supporting the theory of noise-enhanced signal processing and offering new perspectives and tools for future studying complex information encoding in neural systems. By constructing an ion channel blockage model, the effects of potassium and sodium ions on the frequency characteristics of multi-compartment neurons are analyzed and the special influences of calcium ions are revealed. Using the ion channel noise model, the stochastic resonance is investigated, supporting the theory that the noise enhances signal processing. This research offers a new perspective and tool for studying the complex information encoding in neural systems.

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.

Comparison Between Effects of Galvanic and Vibration-Based Vestibular Stimulation on Postural Control and Gait Performance in Healthy Participants: A Systematic Review of Cross-Sectional Studies.

Electricity and vibration were two commonly used physical agents to provide vestibular stimulation in previous studies. This study aimed to systematically review the effects of galvanic (GVS) and vibration-based vestibular stimulation (VVS) on gait performance and postural control in healthy participants. Five bioscience and engineering databases, including MEDLINE via PubMed, CINAHL via EBSCO, Cochrane Library, Scopus, and Embase, were searched until March 19th, 2023. Studies published between 2000 and 2023 in English involving GVS and VVS related to gait performance and postural control were included. The procedure was followed via the Preferred Reporting Items for Systematic reviews and Meta-Analyses guidelines. The methodological quality of included studies was assessed using the NIH study quality assessment tool for observational cohort and cross-sectional studies. A total of 55 cross-sectional studies met the inclusion criteria and were included in this study. Five studies were good-quality while 49 were moderate-quality and 1 was poor-quality. There were 50 included studies involving GVS and 5 included studies involving VVS. GVS and VVS utilized different physical agents to provide vestibular stimulation and demonstrated similar effects on vestibular perception. Supra-threshold GVS and VVS produced vestibular perturbation that impaired gait performance and postural control, while sub-threshold GVS and VVS induced stochastic resonance phenomenon that led to an improvement. Bilateral vestibular stimulation demonstrated a greater effect on gait and posture than unilateral vestibular stimulation. Compared to GVS, VVS had the characteristics of better tolerance and fewer side effects, which may substitute GVS to provide more acceptable vestibular stimulation.

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.