Stochastic Resonance Phenomenon Research Articles

Noise-induced enhancement of stability and resonance in a tri-stable system with time-delayed feedback

In this paper, the mean first-passage times and the stochastic resonance in an asymmetric tri-stable system are studied by considering time-delayed feedback, which is driven by a periodic signal and correlated noises. Both the theoretical expressions for small time delay and the numerical results for large time delay are provided to explore the noise-induced enhancement in stability and resonance. The obtained results suggest that the correlation between the additive and multiplicative noises plays a constructive role on system dynamical behaviors, such as the appearing of noise enhanced stability and stochastic resonance, which can be optimized by choosing proper time-delayed feedback gain for fixed time delay. When the feedback gain is fixed, the time delay can greatly accelerate the crossing between left well and middle well, while cannot effectively enhance the crossing velocity between right well and middle well. Moreover, for small time delay, theoretical analysis predicts that stochastic resonance effect and control performance can be substantially improved by choosing appropriate combination of time delay and feedback gain. For large time delay, the phenomenon of stochastic resonance is enhanced by selecting small feedback gain and large asymmetry.

Adaptive progressive learning stochastic resonance for weak signal detection

Stochastic resonance (SR) can enhance signals by using noise. This has attracted more attention in the field of weak signal detection. In practical applications, owing to the non-adjustability of noisy signals, SR is required to adjust the system parameters adaptively to satisfy the conditions of the SR phenomenon. In this paper, an adaptive progressive learning SR method is proposed to improve the detection ability for weak signal, and the SR phenomenon is quantitatively defined. A theoretical learning framework is established with an improved reinforcement learning model by mapping the nonlinear system parameter space to a progressive learning set. By selecting a proper learning layer within a determined constraint range, the matching system parameters can be quickly and accurately searched to generate a desired optimal output. Numerical simulation results show that the signal energy and the output signal-to-noise ratio (SNR) can be enhanced significantly, which reflects an excellent weak signal detection performance especially for low SNR conditions. Finally, a diagnosis of the outer race fault signals of a rolling bearing confirms that the proposed method can effectively detect fault characteristics.

Abnormal thermal conduction and stochastic resonance phenomenon in a finite lattice system

This paper studies the thermal conduction of Frenkel–Kontorva (FK)-ϕ4 lattices with the finite number of atoms under a periodic force. Through numerical simulations, we find that in the thermal conduction of non-linear lattices, external periodic signals can act in conjunction with noise to create stochastic resonance behaviors and that some adjustable dynamical parameters, such as the onsite potential of the FK and ϕ4 lattices, the amplitude and frequency of external periodic signals, can regulate heat flux. Our study results can provide a sufficient theoretical basis for the fabrication of thermal devices and the control and utilization of thermal energy.

A Comparative Study of Stochastic Resonance Phenomenon under Diffusive and Direct Coupling

In this study, our concern is to compare and analyze stochastic resonance phenomenon in a pair of overdamped systems under two types of coupling: direct and diffusive. Under both types of coupling, we obtain the amplitude of average response of coupled systems, and SR is confirmed from non-monotonic behavior of amplitude with respect to noise level in command of linear stability. In direct interaction, coupling strength and noise level in stochastic resonance vary nearly over a straight line with negative slope whereas in diffusive coupling the behavior is contrasting. In addition, we analyze the asymptotic behavior of second moment and average response of mean field and it is found that the mean field variable exhibits SR only in direct coupling.

Stochastic resonance of double fractional-order coupled oscillator with mass and damping fluctuations

In this study, the stochastic resonance phenomenon of a coupled double fractional-order harmonic oscillator with mass and damping fluctuation is investigated. Firstly, the Shapiro-Loginov formula and Laplace transform are used to obtain the analytical expression of the output amplitude gain of the system output. On this basis, aiming at the key factors involved in the model, including the coupling structure, fractional system, random fluctuation and external periodic force, the influence of coupling coefficient, double fractional order and driving frequency on the output amplitude gain (OAG) is analyzed, and reasonable physical explanations are provided. Secondly, numerical simulations are carried out to verify the accuracy of the theoretical solutions. The simulation results show that under certain conditions, the OAG of the system can appear stochastic resonance phenomenon with the above parameters, especially: (1) The OAG with the change of external drive frequency appears double peak, single peak and single valley stochastic resonance phenomenon, which does not appear under the same external disturbance with integer order and uncoupled conditions; (2) The order of double fractional derivative significantly affects the variation trend of OAG; (3) The coupling coefficient is not sensitive to the OAG.

Diffusive behavior of a coupled generalized Langevin system under bounded noise

In this paper, the phenomenon of diffusion induced by bounded noise is studied in a coupled generalized Langevin system. Analytical expressions for the moment of the response are derived by means of Laplace transform. The obtained results indicate the existence of the non-Markovian diffusion. Specifically, the coupling strength between harmonic oscillators and the intensity added to Wiener process play opposite roles in the transition from the stationary to the diffusive regime. Also, the effects of the amplitude of bounded noise and the cross-correlation between noises are analyzed. Moreover, the phenomenon of stochastic resonance (SR) is found by the index of signal-to-noise ratio (SNR). Interestingly, the increase of coupling damping coefficient enhances diffusive behavior but suppresses SR. Finally, the numerical results well verify the validity of the theoretical analyses.

Research and Application of a Novel Combined Asymmetric Tristable Stochastic Resonance System

Aiming at the deficiency of weak signal amplification ability in traditional bistable system and combining with the advantages of tristable system and asymmetric system, three novel of combined asymmetric tristable stochastic resonance (SR) systems are proposed by combining the classical bistable potential model with the Gaussian potential model in this paper, namely, asymmetric well depth stochastic resonance (AWDSR), asymmetric well width stochastic resonance (AWWSR) and asymmetric well depth width stochastic resonance (AWDWSR). The stochastic resonance phenomena of the above three systems under [Formula: see text] noise with the influence of parameters are analyzed, respectively. Through empirical mode decomposition and adaptive genetic algorithm to optimize the parameters for weak signal extraction, it can be found that this method can achieve stronger SR performance. After the bearing fault diagnosis of the proposed systems, the detection results of the three asymmetric systems are obviously better than the classical tristable stochastic resonance (CTSR) and symmetric stochastic resonance (SSR), and the performance advantage of AWDWSR is the greatest. This can provide some reference value for practical engineering application.

Noise-induced synchronization stochastic resonance in Hodgkin–Huxley neurons

In this paper, based on the Hodgkin–Huxley (H-H) neuron model, three distinct types of noises are introduced into the input of the neuron. The noises are Gaussian white noise (GWN), Lévy noise and Colored noise, separately. The phenomenon of stochastic resonance under and above threshold in one-dimensional H-H neuron is discussed. First, the responses of H-H neuron to different input signal frequency, amplitude and constant offset stimulation are researched. The neuron membrane potential diagram and spectrum diagram are given. Then, the mutual information rate (MIR) is taken as the evaluation index. The results show that adding a noise of certain intensity can increase the response of neuron to the orignal signal and the MIR between the output and input of neuron has unimodal property, which proves the existence of stochastic resonance under and above the threshold. We also find that neurons have frequency selectivity and different transmission performance for different amplitude of input signals. In addition, the constant offset stimulus should not be too large. Finally, it is discovered that the adaptability of subthreshold stochastic resonance and suprathreshold stochastic resonance (SSR) characteristics characteristics of one-dimensional H-H neurons induced by three distinct types of noises is different. What is more important is that the results of this paper will be instrumental in the future researching on the affect of these three noises in the stochastic resonance of neuron networks.

Collective dynamic behaviors of a general adjacent coupled chain in both unconfined and confined spaces

This paper studies the collective dynamic behaviors of a general adjacent coupled chain under a periodic driving force and dichotomous noise in both unconfined and confined spaces. The precise conditions for the stability, synchronization, and stochastic resonance (SR) of the system in an unconfined space were analytically derived and verified by numerical algorithms. The stability and synchronization of the adjacent coupled chain in the unconfined space were found to be related to the system and noise parameters. The collective dynamic behaviors of the adjacent coupled chain in the confined space were also analyzed through numerical simulations, and it was found that due to boundary constraints, the adjacent coupled chain consistently achieves stability and synchronization in the confined space. Moreover, when compared with the unconfined system, the output amplitude of the confined system exhibits more complex SR phenomena, such as double-peak SR, multi-peak SR, superharmonic SR and so on.

Studying Stochastic Resonance Phenomenon in the Fractional-Order Lorenz-Like Chaotic System

At present, stochastic resonance (SR) based on Duffing and Langevin equations has been widely studied, but there is little research on SR phenomenon in higher-dimensional fractional-order systems. Based on the fractional-order Lorenz-like system, the SR phenomenon is studied from the perspective of equilibrium point in this paper. The dynamic process of SR phenomenon is presented, and several key parameters are derived. The results of numerical simulation show that the boundary of SR and chaos system will be broken if the order of the fractional-order system or internal parameters is properly adjusted, and the effect of SR phenomenon will also be influenced. This paper connects two important nonlinear phenomena (chaos and SR) based on the fractional-order system, which provides a new idea for the conversion between chaos and SR systems.

Noise-tuned bursting in a Hedgehog burster.

Noise can shape the firing behaviors of neurons. Here, we show that noise acting on the fast variable of the Hedgehog burster can tune the spike counts of bursts via the self-induced stochastic resonance (SISR) phenomenon. Using the distance matching condition, the critical transition positions on the slow manifolds can be predicted and the stochastic periodic orbits for various noise strengths are obtained. The critical transition positions on the slow manifold with non-monotonic potential differences exhibit a staircase-like dependence on the noise strength, which is also revealed by the stepwise change in the period of the stochastic periodic orbit. The noise-tuned bursting is more coherent within each step while displaying mixed-mode oscillations near the boundaries between the steps. When noise is large enough, noise-induced trapping of the slow variable can be observed, where the number of coexisting traps increases with the noise strength. It is argued that the robustness of SISR underlies the generality of the results discovered in this paper.

Collective Behaviors of Star-Coupled Harmonic Oscillators with Fluctuating Frequency in the Presence of Stochastic Resonance

The stochastic resonance (SR) of a star-coupled harmonic oscillator subject to multiplicative fluctuation and periodic force in viscous media is studied. The multiplicative noise is modeled as a dichotomous noise and the memory of viscous media is characterized by a fractional power kernel function. By using the Shapiro–Loginov formula and Laplace transform, we obtain the analytical expressions of the first moment of the steady-state response and study the relationship between the system response and the system parameters in the long-time limit. The simulation results show the nonmonotonic dependence between the response output gain and the input signal frequency, the noise parameters of the system, etc., which indicates that the bona fide resonance and the generalized SR phenomena appear. Furthermore, the fluctuation noise, the number of particles, and the fractional order work together, producing more complex dynamic phenomena compared with the integral-order system. In addition, all the theoretical analyses are supported by the corresponding numerical simulations. We believe that the results that we have found may be a certain reference value for the research and development of the SR.

Entropic stochastic resonance and super-harmonic stochastic resonance in a dichotomous fluctuating potential

When a Brownian particle moves in a confined space, the boundaries of the confined space can form an entropic barrier and thus induce the classical entropic stochastic resonance (ESR) phenomenon. This paper introduces a dichotomous fluctuating potential into the classical ESR model and studies the dynamics and ESR phenomena of the confined particle. It is shown that the amplitude of each harmonic component of both the horizontal and vertical displacements of the confined particle appears in various types of ESR phenomena, such as single-peak ESR, double-peak ESR, or even multi-peak ESR. This multi-peak ESR phenomenon is caused when the different dynamical states of the confined particle (under the joint action of the energy and entropy potentials) reach the optimal equilibrium. The results of this paper will help to understand the mechanism of stochastic dynamics of particles in confined spaces.

A perspective on ab initio modeling of polaritonic chemistry: The role of non-equilibrium effects and quantum collectivity.

This Perspective provides a brief introduction into the theoretical complexity of polaritonic chemistry, which emerges from the hybrid nature of strongly coupled light-matter states. To tackle this complexity, the importance of ab initio methods is highlighted. Based on those, novel ideas and research avenues are developed with respect to quantum collectivity, as well as for resonance phenomena immanent in reaction rates under vibrational strong coupling. Indeed, fundamental theoretical questions arise about the mesoscopic scale of quantum-collectively coupled molecules when considering the depolarization shift in the interpretation of experimental data. Furthermore, to rationalize recent findings based on quantum electrodynamical density-functional theory (QEDFT), a simple, but computationally efficient, Langevin framework is proposed based on well-established methods from molecular dynamics. It suggests the emergence of cavity-induced non-equilibrium nuclear dynamics, where thermal (stochastic) resonance phenomena could emerge in the absence of external periodic driving. Overall, we believe that the latest ab initio results indeed suggest a paradigmatic shift for ground-state chemical reactions under vibrational strong coupling from the collective quantum interpretation toward a more local, (semi)-classically and non-equilibrium dominated perspective. Finally, various extensions toward a refined description of cavity-modified chemistry are introduced in the context of QEDFT, and future directions of the field are sketched.

Nonbistable rectified linear unit-based gain-dissipative Ising spin network with stochastic resonance effect

The gain-dissipative Ising machine (GIM), comprising a nonlinear transfer function and spin interaction feedback, is one of the most promising quantum analog annealers. However, previous GIM constructions have been limited to only bistable nonlinear transfer functions with low noise intensity condition. To provide a new insight and broaden the potential design of GIMs, we construct a nonbistable rectified linear unit-based gain-dissipative Ising spin network (RISN). In contrast to the traditional GIM, spin dynamics analysis in the uncoupled state proves that RISN is nonbistable. Furthermore, it is demonstrated that the proposed RISN can effectively solve combinatorial optimization problems with a high noise level, which can be regarded as a stochastic resonance phenomenon. The proposed configuration, which does not comply with known conclusions, can become a stepping-stone for new GIM designs.

A New Piecewise Nonlinear Asymmetry Bistable Stochastic Resonance Model for Weak Fault Extraction

In order to solve output saturation problems found in traditional stochastic resonance methods and to improve the diagnosis ability of weak faults, a new piecewise nonlinear asymmetric bistable stochastic resonance (PNABSR) method is proposed. This model uses a left and right potential function with an asymmetrical shape, which makes it easier to induce stochastic resonance phenomena. Based on the PNABSR model, the expression of the signal-to-noise ratio (SNR) is derived, and the changes in the SNR with different parameters in the PNABSR model are analyzed. Then, the parameters in the PNABSR model are optimized using the adaptive intelligent algorithm to enhance the diagnostic ability. The diagnosis properties of the weak fault are compared between the PNABSR model and the classical bistable stochastic resonance model (CBSR). The experimental results prove that the PNABSR model can effectively extract the weak fault characteristic frequency under a strong noise background, verifying the effectiveness of this method.

A Magnet-Coil-Type Bistable Vibration Energy Harvester for Random Wave Environment

In this study, a new bistable vibration energy harvesting system is developed by originally proposing a bistable vibration model comprising a spring and a mass block and then applying a vibration generator composed of a coil and a magnet. The nonlinear equations of motion for this vibration energy harvesting system are developed and the static potential energy distribution is analyzed. The bistable vibration characteristics and the method for prediction of the periodic excitation frequency at which stochastic resonance is likely to occur are investigated theoretically, and the electromagnetic induction-based bistable vibration energy harvesting system is then developed. We predicted the excitation value that the stochastic resonance phenomenon is most likely to occur at 1.543 Hz. We also conducted experiments at 1.15 Hz, 1.50 Hz, and 1.85 Hz, which are centered on the predicted value. As a result, stochastic resonance occurred in all experimental cases. The power generation efficiency was improved by 125.03%, 149.05%, and 95.39%, respectively.

Exhibition of Noise-Aided Stochastic Resonance by Discontinuity Detectors in Smartphone Images

The use of smartphone cameras for capturing photographs has seen an exponential growth in the last decade. The noise present in these photographs significantly deviates from the popular Independently Identically Distributed (i.i.d.) Additive White Gaussian Noise (AWGN) noise, and thus the conclusions drawn from simulated-AWGN cannot be directly applied to the smartphone’s true noise. This paper is the first reporting of the exhibition of Stochastic Resonance (SR) or noise-induced threshold-crossing in three genres of discontinuity detectors used in image processing — corner detector, line detector, and edge detector for real-world smartphone images. For the images under investigation, the performance of these detectors is quantified w.r.t. parameters representing intrinsic noise. Observations suggest that all these detectors inherently exhibit the phenomenon of SR due to the fundamental assistance offered by controlled amount of noise in crossing detector thresholds. The manifestations of SR — constant parameter value with varying noise and varying parameter value with constant noise — are demonstrated to exhibit SR in each of the three detectors.

Non-Gaussian noise and autapse-induced inverse stochastic resonance in bistable Izhikevich neural system under electromagnetic induction

Inverse stochastic resonance refers to the phenomenon that the average firing rate of a neuron is inhibited by noise, of which mechanism is widely used in a variety of biological cells and economic phenomena. In this paper, a bistable Izhikevich neural model and triple-neuron feed-forward loop Izhikevich neural network motifs under the effects of electromagnetic induction are constructed to investigate the phenomenon of inverse stochastic resonance induced by Non-Gaussian colored noise and electrical autapse. It is found that there exists a minimum value of the average firing rate curve caused by intensity of non-Gaussian colored noise, which is the phenomenon of inverse stochastic resonance. Obtained results also show that the inverse stochastic resonance induced by electrical autapse shows a decaying oscillation process with respect to synaptic delay time, and further research indicates that average firing rate has several minimums as a function of time delay of electrical autapse, which is called multiple inverse stochastic resonance. Furthermore, the inverse stochastic resonance in triple-neuron feed-forward loop Izhikevich neural network motifs are also examined, and it is confirmed that the responses of single Izhikevich neuron and neural network motifs to different parameters show consistency under same conditions, but also show some differences. Finally, the effects of electromagnetic induction on inverse stochastic resonance are checked both in single Izhikevich neural model and feed-forward loop network motifs. Electromagnetic induction feedback gain coefficient k1 should not be too large under certain conditions, otherwise it may cause FFL network motifs to loss the function of suppressing the discharge activity. No matter how the values of electromagnetic induction parameter k2 and magnetic flux leakage coefficient k3 change, they basically cannot affect the ISR in the feed-forward loop neural network motifs The conclusions of this paper may help researchers understanding how using unique mechanism of inverse stochastic resonance to find advantages and avoid disadvantages in biomedical field and many interdisciplinary research.

Double stochastic energetic resonance of underdamped two-scale bistable system

Multistable structures have abundant nonlinear characteristics, a multi-level system with large-scale and small-scale bistable structures is constructed, and its dynamic characteristic is discussed. Based on the complete Langevin equation with an inertial term and a variable damping term, the relationship between the Kramers escape rate and the damping coefficient is deduced and the approximate analytical expression of the output response in the underdamped state is established. From the view of the energy, the mechanism of double resonance and resonance effect enhancement induced by damping is further revealed with the energy dissipation caused by damping as the core. The physical quantity work is introduced to measure the strength of the resonance effect. The results of theoretical analysis and numerical simulation indicate that as the damping coefficient decreases into the underdamping or even the weak damping scope, the double stochastic resonance phenomenon induced by noise still exists. The strongest resonance effect can be obtained with the optimal damping value.