Stochastic Resonance Phenomenon Research Articles

Improving the Stochastic Resonance in a Bistable System with the Bounded Noise Excitation

The stochastic resonance (SR) phenomenon is investigated in a typical bistable system that excited by the bounded noise and the weak low-frequency signal simultaneously. Based on numerical simulations, the main results are obtained. The SR performance mainly depends on the mean frequency and is influenced by the randomness level of the bounded noise. It occurs when the mean frequency is much larger than or approximates the signal frequency. However, the SR almost disappears when the mean frequency is much smaller than the signal frequency. By introducing an auxiliary high-frequency signal in the excitations, another phenomenon called as vibrational resonance (VR) appears. With the cooperation of VR, the SR performance is greatly improved. The results in this paper give a reference to deal with the weak signal submerged in the bounded noise.

Stochastic Dynamical Behaviors for a Time-Delayed Insect Outbreak System with a Periodic Signal Subjected to Multiplicative and Additive Noises

In this paper, our aim is to investigate the steady state behaviors, the stochastic resonance (SR) phenomenon and the mean decline time for a biological insect growth system induced by the terms of time delay, the multiplicative and additive noises. Numerical results indicate that the multiplicative noise and the additive one can both weaken the stability of the biological system and accelerate the depression process of the insect population, while time delay can strengthen the stability of the insect growth system and prolong the lifetime of the insect system. With respect to the SR phenomenon caused by time delay, noise terms and the weak periodic signal, the results show that some interesting dual peak phenomena for the signal-to-noise ratio (SNR) occur frequently. Specific contents are as follows: In SNR-[Formula: see text] plots, the additive noise intensity [Formula: see text] and time delay [Formula: see text] can easily induce the phenomenon of dual peaks, while in the SNR-[Formula: see text] plots, the multiplicative noise intensity [Formula: see text] and time delay [Formula: see text] can both reduce the SR effect distinctly. On the other hand, in the SNR-[Formula: see text] plots, when either of [Formula: see text] or [Formula: see text] takes a big value, the other plays a negative role in stimulating the SR phenomenon; while either of them takes a small value, the other can excite a significant effect of double peaks.

Collective behavior and stochastic resonance in a linear underdamped coupled system with multiplicative dichotomous noise and periodical driving

In this paper the collective behavior and stochastic resonance (SR) phenomenon in a linear underdamped coupled system with multiplicative dichotomous noise and periodical driving is investigated. Firstly, the stationary solution of the mean field and the stability conditions of the system are obtained by introducing the mean field of the system. Secondly, the collective behaviors of the particles are discussed through studying their synchronization behavior. Finally, the range of parameters for which the SR phenomenon occurs in the system is given, based on the stability conditions. The synchronous behaviors of particles and SR phenomenon, as well as the concrete influence of coupling on the system are analyzed by numerical simulations.

Impact of colored cross-correlated noises on stochastic resonance and mean extinction rate for a metapopulation system with a multiplicative periodic signal

In this paper, we aim to explore the mean extinction rate and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by a multiplicative periodic signal, colored cross-correlated multiplicative and additive Gaussian noises. By use of the fast descent method and the adiabatic approximation theory for the signal-to-noise ratio, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results indicate that the various SR phenomena occur in the metapopulation system due to the variation of the noise terms and the correlation time. Specifically, the noise correlation always plays a critical role in motivating the SR phenomenon, while the multiplicative noise exerts the inhibition effect on the SR. Interestingly, the weak additive noise can stimulate the resonant peak of the SNR, while the further increase of the noise intensity will lead to the reduction of the SR effect. On the other hand, the noise correlation time τ plays antipodal roles in motivating the SR phenomenon under different circumstances. With regard to the mean extinction rate of the population from the boom state to the extinction one, by performing the numerical calculations, it is found that the additive noise always accelerate the extinction of the population, while the correlation noise will slow down the decline for the population. The role that the noise correlation time plays in the population extinction depends on the values that λ takes.

Stochastic resonance in a time-delayed tumor cell growth system driven by additive and multiplicative noises

In this paper, the stochastic resonance (SR) phenomenon in a time-delayed tumor cell growth system subjected to a multiplicative periodic signal, the multiplicative and additive noise is investigated. By applying the small time-delay method and two-state theory, the expressions of the mean first-passage time (MFPT) and signal-to-noise ratio (SNR) are obtained, then, the impacts of time delay, noise intensities and system parameters on the MFPT and SNR are discussed. Simulation results show that the multiplicative and additive noise always weaken the SR effect; while time delay plays a key role in motivating the SR phenomenon when noise intensities take a small value, it will restrain SR phenomenon when noise intensities take a large value; the cycle radiation amplitude always plays a positive role in stimulating the SR phenomenon, while, system parameters play different roles in motivating or suppressing SR under the different conditions of noise intensities.

Stochastic resonance in an under-damped linear system with nonlinear frequency fluctuation

Stochastic resonance (SR) in a second-order under-damped linear system with nonlinear frequency fluctuation is investigated, and the nonlinear frequency fluctuation is modeled as dichotomous noise. Firstly, by the use of the Shapiro–Loginov formula and the Laplace transform technique, the analytical expression for the average amplitude gain of the system output is obtained. Then, the non-monotonic behaviors of the average amplitude gain are analyzed. Finally, numerical simulations are presented to verify the effectiveness of the analytical results. Simulation results show that, with the variations of system parameters and noise parameters, the average amplitude gain shows SR and multi-SR phenomena. In addition, the bona fide resonance can be observed by adjusting the frequency fluctuation coefficients. In conclusion all the results show that the nonlinear character of frequency fluctuation plays a key role in system’s resonance behavior. Therefore, by introducing nonlinear frequency fluctuation into the linear system, we can control SR in the system in a certain range, and it has promising feasibility in practical engineering application.

Collective stochastic resonance behavior in the globally coupled fractional oscillator

This study investigates the collective stochastic resonance (SR) behavior of globally coupled fractional Langevin equations with multiplicative noise and external signal. We define the mean field S(t) and derive the steady-state output amplitude $$A_{1}$$ of the first moment $$\langle S(t)\rangle $$ by using the stochastic average method. We characterize the effects of fractional order, intrinsic frequency, noise correlation rate, and driving frequency on the steady-state output amplitude $$A_{1}$$ as a function of noise intensity. We observe that the collective SR phenomenon occurs in a fractional coupled stochastic dynamic system. We also demonstrate that collective SR behavior versus noise intensity can ensue when system parameters satisfy the necessary and sufficient conditions; this notion means that we can control the collective SR of our fractional dynamic model by properly adjusting the system parameters within a certain range. This study verifies the reliability and effectiveness of the theoretical results by various numerical simulations. Our results on SR in a globally coupled fractional harmonic oscillator provide useful information in modern science.

Stochastic resonance in time-delayed exponential monostable system driven by weak periodic signals

Based on the exponential monostable potential, we study an exponential monostable system with time-delayed feedback driven by weak periodic signals and additive Gaussian white noises. The small delay approximation is used to deduce the steady-state probability distribution and the effective potential function is derived. The system parameters l and b, time delay τ, feedback strength β can change the shapes of the potential function. The mean first-passage time (MFPT) is calculated, which plays an extremely important role in the research of particles escape. And the signal-to-noise ratio (SNR) of the system can be obtained by using the adiabatic approximation theory. The phenomenon of stochastic resonance is investigated under different system parameters and time-delayed feedback. The amplitude of SNR can be changed by adjusting the system parameters. When the feedback strength β is positive (or negative), the time delay τ can promote (or suppress) the stochastic resonance phenomenon. The SNR versus the noise intensity D presents the stochastic resonance phenomenon. In addition, the SNR increases non-monotonically with the increasing feedback strength β and the parameter b. Also, the analysis and numerical simulation results of SNR are in good agreement with the formula simulation.

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

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

Enhancement of target location rates by stochastic modulation of Brownian motion

The binding of proteins to target sites on DNA, an important trigger of regulatory changes in a cell’s life cycle, is a complex biophysical process that is sensitive to details of the surroundings in which it takes place. It is affected, in particular, and among other factors, by thermal noise, by the random binding and unbinding of the protein to the polynucleotide chain, by fluctuations in the chain’s conformations, and by the degree of molecular crowding around the reacting species. In this paper, using a model based on dynamically disordered Brownian motion (a model previously introduced to explain the occasional occurrence of non-Gaussian effects in simple random walk behaviour), we show that one such factor—the internal dynamics of DNA—can enhance the rate at which a target on the chain is located by a particle moving randomly along its contour. The enhancement of the target location rate is reminiscent of the phenomenon of stochastic resonance, in that it occurs when the timescale characteristic of the chain’s relaxation matches the timescale of the particle’s motion. This finding is in qualitative agreement with the few experimental and numerical results to which it can be loosely compared.

Coherent neural oscillations induced by weak synaptic noise

We analyze the effect of synaptic noise on the dynamics of the FitzHugh–Nagumo (FHN) neuron model. In our deterministic parameter regime, a limit cycle solution cannot emerge through a singular Hopf bifurcation, but such a limit cycle can nevertheless arise as a stochastic effect, as a consequence of weak synaptic noise in a regime of strong timescale separation (varepsilon rightarrow 0) between the slow and fast variables of the model. We investigate the mechanism behind this phenomenon, known as self-induced stochastic resonance (SISR) (Muratov et al. in Physica D 210:227–240, 2005), by using multiple-time perturbation techniques and by analyzing the escape mechanism of the random trajectories from the stable manifolds of the model equation. Even though SISR occurs only in the limit as the singular parameter varepsilon rightarrow 0, decreasing varepsilon does not increase the coherence of the oscillations in the FHN model, but rather increases the interval of the noise amplitude sigma for which coherence occurs. This is in contrast to the dynamical system studied in Muratov et al. (2005). Moreover, the phenomenon is robust under parameter tuning. Numerical simulations exhibit the results predicted by the theoretical analysis. In fact, our analysis together with that in Yamakou and Jost (Weak noise-induced transitions with inhibition and modulation of neural oscillations, 2017) reveals that the FHN model can support different stochastic resonance phenomena. While it had been known (Pikovsky and Kurths in Phys Rev Lett 78:775–778, 1997) that coherence resonance can occur when the slow variable is subjected to noise, we show that, when noise is added to the fast variable, two other types, inverse stochastic resonance and SISR, may emerge in the same weak noise limit and that the transition between these phenomena can be induced by varying a simple parameter.

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal**Project supported by the National Natural Science Foundation of China (Grant No. 11772048).

Stochastic resonance (SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory (LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density (PSD) and signal-to-noise ratio (SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.

Effect of noise stimulation below and above sensory threshold on postural sway during a mildly challenging balance task

BackgroundMechanical and electrical sub-sensory noise stimulation applied to the sensory receptors has been shown to improve performance during postural balance tasks. This improvement has been linked with the Stochastic Resonance (SR) phenomenon. It is not clear if noise levels above sensory threshold can also lead to a reduction in postural sway. Research questionThe aim of this study was to investigate the different effects of sub- and super-sensory electrical noise stimulation applied to the Tibialis Anterior muscle during several repetitions of a mildly challenging single-leg postural balance task. MethodsFifteen healthy individuals participated in this study. Participants performed 25 repetitions of a balance tasks where they leaned forward and maintained a pre-determined position for 20 s. Each participant experienced 5 different stimulation levels (no-stimulation, 70%, 90%, 110% and 130% of their sensory threshold ST) for 5 times in a randomized order. Optimal stimulation (OS) was defined as the stimulation intensity minimizing the standard deviation of postural sway in the anteroposterior direction. Results∼57% of the participants presented levels of OS below ST. We did not observe a clear SR-effect, characterized by a U-shaped relationship between the performance metric and the stimulation intensity. OS led to a selective improvement in all the anteroposterior posturographic parameters analyzed. Stimulation below ST led to an improvement in most of the balance features, while stimulation above ST led to an increase in postural sway. SignificanceOur results suggest that OS can be found both below and above ST although stimulation below ST appears to be more effective in reducing postural sway.

Suprathreshold Stochastic Resonance behind Cancer

Noise in gene expression is pervasive and, in some cases, even fulfills a functional role. Cancer cell populations exploit noise to increase heterogeneity as a defense against therapies. What lies behind this picture is a phenomenon of stochastic resonance led by the collective, rather than by individual cells.

Efficacy of Stochastic Vestibular Stimulation to Improve Locomotor Performance During Adaptation to Visuomotor and Somatosensory Distortion.

Astronauts exposed to microgravity face sensorimotor challenges affecting balance control when readapting to Earth's gravity upon return from spaceflight. Small amounts of electrical noise applied to the vestibular system have been shown to improve balance control during standing and walking under discordant sensory conditions in healthy subjects, likely by enhancing information transfer through the phenomenon of stochastic resonance. The purpose of this study was to test the hypothesis that imperceptible levels of stochastic vestibular stimulation (SVS) could improve short-term adaptation to a locomotor task in a novel sensory discordant environment. Healthy subjects (14 males, 10 females, age = 28.7 ± 5.3 years, height = 167.2 ± 9.6 cm, weight = 71.0 ± 12.8 kg) were tested for perceptual thresholds to sinusoidal currents applied across the mastoids. Subjects were then randomly and blindly assigned to an SVS group receiving a 0–30 Hz Gaussian white noise electrical stimulus at 50% of their perceptual threshold (stim) or a control group receiving zero stimulation during Functional Mobility Tests (FMTs), nine trials of which were done under conditions of visual discordance (wearing up/down vision reversing goggles). Time to complete the course (TCC) was used to test the effect of SVS between the two groups across the trials. Adaptation rates from the normalized TCCs were also compared utilizing exponent values of power fit trendline equations. A one-tailed independent-samples t-test indicated these adaptation rates were significantly faster in the stim group (n = 12) than the control (n = 12) group [t(16.18) = 2.00, p = 0.031]. When a secondary analysis was performed comparing “responders” (subjects who showed faster adaptation rates) of the stim (n = 7) group to the control group (n = 12), independent-samples t-tests revealed significantly faster trial times for the last five trials with goggles in the stim group “responders” than the controls. The data suggests that SVS may be capable of improving short-term adaptation to a locomotion task done under sensory discordance in a group of responsive subjects.

On a “deterministic” explanation of the stochastic resonance phenomenon

The present paper concerns the analysis of the stochastic resonance phenomenon that previously has been thoroughly studied and found numerous applications in physics, neuroscience, biology, medicine, mechanics, etc. A novel “deterministic” explanation of this phenomenon is proposed that allows broadening the range of dynamical systems for which the phenomenon can be predicted and analysed. Our results indicate that stochastic resonance, similarly to vibrational resonance, arises due to deterministic reasons: it occurs when a system is excited with two (or more) vastly different frequencies, one of which is much higher than another. The effective properties of the system, e.g. stiffness or mass, change under the action of the high-frequency excitation; and the low-frequency excitation acts on this “modified” system leading to low-frequency resonances. In the case of a broadband random excitation, the high-frequency part of the excitation spectrum affects the effective properties of the system. The low-frequency part of the spectrum acts on this modified system. Thus by varying the noise intensity one can change properties of the system and attain resonances. This explanation allows using “deterministic” approach, i.e. replacing noise by high-frequency excitation, when studying the stochastic resonance phenomenon. Employing this approach, we demonstrate that linear and nonlinear stochastic systems with varying parameters, i.e. parametrically excited systems, can exhibit the phenomenon and determine the corresponding resonance conditions.

Stochastic resonance in a time-delayed feedback tristable system and its application in fault diagnosis

Stochastic resonance (SR) phenomena in a time-delayed feedback tristable system driven by Gaussian white noise are investigated by simulating the potential function, mean first-passage time (MFPT), and signal-to-noise ratio (SNR) of the system. Through the use of a short delay time, the generalized potential function and stationary probability density function (PDF) are obtained. The delay feedback term has a significant effect on both equations, and that the parameters b, c, and d have different effects on the three wells of the potential function. The MFPT is calculated, which plays an extremely important role in research on particles escape rates. We find that the delay feedback term can affect the noise enhanced stability (NES). In addition, the SR characteristics are studied by the index of SNR. The simulation demonstrates that SNR is a non-monotonic distributed and that the peak SNR value can be attained by adjusting the appropriate parameters. Finally, the proposed theory is combined with a variable step method and applied to the detection of high frequencies in experiments. The result indicates that the fault frequency can be identified, and that the energy of the fault signal can be enhanced under suitable delay feedback parameters.

Stochastic resonance and synchronization behaviors of excitatory-inhibitory small-world network subjected to electromagnetic induction**Project supported by the National Natural Science Foundation of China (Grant No. 11172103).

The phenomenon of stochastic resonance and synchronization on some complex neuronal networks have been investigated extensively. These studies are of great significance for us to understand the weak signal detection and information transmission in neural systems. Moreover, the complex electrical activities of a cell can induce time-varying electromagnetic fields, of which the internal fluctuation can change collective electrical activities of neuronal networks. However, in the past there have been a few corresponding research papers on the influence of the electromagnetic induction among neurons on the collective dynamics of the complex system. Therefore, modeling each node by imposing electromagnetic radiation on the networks and investigating stochastic resonance in a hybrid network can extend the interest of the work to the understanding of these network dynamics. In this paper, we construct a small-world network consisting of excitatory neurons and inhibitory neurons, in which the effect of electromagnetic induction that is considered by using magnetic flow and the modulation of magnetic flow on membrane potential is described by using memristor coupling. According to our proposed network model, we investigate the effect of induced electric field generated by magnetic stimulation on the transition of bursting phase synchronization of neuronal system under electromagnetic radiation. It is shown that the intensity and frequency of the electric field can induce the transition of the network bursting phase synchronization. Moreover, we also analyze the effect of magnetic flow on the detection of weak signals and stochastic resonance by introducing a subthreshold pacemaker into a single cell of the network and we find that there is an optimal electromagnetic radiation intensity, where the phenomenon of stochastic resonance occurs and the degree of response to the weak signal is maximized. Simulation results show that the extension of the subthreshold pacemaker in the network also depends greatly on coupling strength. The presented results may have important implications for the theoretical study of magnetic stimulation technology, thus promoting further development of transcranial magnetic stimulation (TMS) as an effective means of treating certain neurological diseases.

A new robust watermarking system in integer DCT domain

In this paper, a robust watermarking technique is proposed using integer discrete cosine transform, non-linear chaotic map and dynamic stochastic resonance (DSR). Firstly, the host image is transformed into integer DCT domain where the coefficients are partitioned into non-over-lapping blocks. A circulant matrix is then constructed from the selected blocks. Block selection is done using a non-linear chaotic map. This circulant matrix is used for embedding the watermark by computing the singular values. The extraction of the watermark is done by producing the dynamic stochastic resonance (DSR) phenomena and casting a verification step. This verification step essentially solves the false positive detection problem that arises in SVD based watermarking. The experimental results demonstrate that the proposed scheme is imperceptible and robust against a variety of intentional or unintentional attacks.