Occurrence Of Stochastic Resonance Research Articles

Langevin’s Equation of Motion: Dynamical States and Stochastic Resonance

In this present work, we numerically observe the existence of two dynamical states of trajectories in the underdamped motion of a particle in an inhomogeneous periodic bistable potential with high friction coefficient driven by a periodic force. The system is inhomogeneous in the sense that the coefficient of friction is periodic in space and with phase difference 'ϕ' with respect to the periodic bistable potential. Just like in sinusoidal potentials, the occurrence of stochastic resonance (SR) in the periodic bistable potential is due to the transitions between the dynamical states at an optimal (thermal) noise strength.

Lévy noise-induced transition and stochastic resonance in Brusselator system

The noise-induced transition and stochastic resonance (SR) phenomenon of Brusselator system under the excitation of Levy noise is investigated in this paper. The Janicki–Weron algorithm is used to simulate Levy noise, and the stationary probability density is obtained by solving the system equation through the fourth-order stochastic Runge–Kutta algorithm. The influences of the noise intensity, stability index and skewness parameter on the stationary probability density are analyzed. The numerical results imply that the stability index, skewness parameter and noise intensity can induce the transition. Moreover, the effects of the stability index and skewness parameter of Levy noise, as well as the amplitude of external signal on the signal-to-noise ratio are discussed. The research results show that the larger stability index, skewness parameter and signal amplitude are beneficial to the occurrence of SR.

Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

The occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker–Planck equation describing the system dynamics, together with the corresponding Ito–Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

Stochastic resonance and free oscillation in a sinusoidal potentials driven by a square-wave periodic force

Recently, the occurrence of stochastic resonance in a sinusoidal potential driven by a sinusoidal force and a Gaussian white noise was experimentally verified. In this work, we experimentally show that stochastic resonance in sinusoidal potentials can also be observed when driven by a square-wave periodic force. The occurrence of stochastic resonance could be explained as due to the appearance of two dynamical states similar to what was done when driven by a sinusoidal force at large frequencies. However, at smaller frequencies of the square-wave drive, the free but damped oscillations of the output could be observed and the effective exponential damping coefficients measured.

Stochastic resonance in deformable potential with time-delayed feedback.

This paper reports the stochastic resonance (SR) phenomenon with memory effects for a Brownian particle in a potential whose shape is subjected to deformation. We model the deformation in the system by the Remoissenet-Peyrard potential and the memory effects by the time-delayed feedback. The question of the possible influence of time-delayed feedback on the occurrence of SR is then of our interest. We examine numerically the effect of feedback strength as well as time delay on SR phenomenon in terms of hysteresis loop area. It is found that time-delayed feedback has a significant effect on SR and can induce double resonances in the system. We show that the properties of SR are varying, depending on interdependence between feedback strength, time delay and shape parameter. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.

Extended analysis of stochastic resonance in a modular neuronal network at different scales

Based on the firing dynamics at three different levels of microscale, mesoscale and macroscale, this study presents an extended analysis of stochastic resonance in a modular neuronal network in the spatially correlated white noise environment. Two well-defined modules of small-world subnetwork and scale-free subnetwork constitute the modular neuronal network in a hierarchical way. When a subthreshold periodic input is incorporated into this network, numerical results illustrate that a collective pattern of stochastic resonance emerges at macroscopic scale when the intensity of the correlated noise is appropriately tuned. Through extended analysis, one can detect that the firing rhythms of individual neurons gradually follow those of the periodic input at microscale. In addition, the occurrence of stochastic resonance at mesoscale in the small-world subnetwork is earlier than that in the scale-free subnetwork, and the peak height of resonance curve in the former subnetwork is remarkably higher than that in the latter one. These combined results indicate that the small-world subnetwork is more favorable than the scale-free subnetwork to induce stochastic resonance in this constructed modular network. The robustness of the extended analysis of stochastic resonance against variations in noise correlation coefficient and intra-module probability is also unveiled. This study provides a new perspective and tool to understand the collective phenomenon of stochastic resonance in realistic neuronal systems.

Stochastic resonance and thermal reversal phenomenon in the thermal conduction of Frenkel–Kontorova lattices

Thermal conduction of Frenkel–Kontorova (FK) lattices with a sustained time periodical force is investigated numerically. The occurrence of stochastic resonance and thermal reversal phenomenon is observed, namely, there exist values of the driving frequency at which the heat flux takes its maximum value and directs a reversal of the heat flux for an average zero-temperature difference between the two contacts in a net. The above phenomena are determined by the dynamical parameters of the model, such as the lattice period, the strength of the on-site potential and so on.

Studies on the signal amplification in weighted and unweighted small-world networks

Weighted and unweighted networks composed of coupled bistable oscillators with small-world topology are investigated under the co-presence of a weak signal and multiplicative Gaussian white noise. As the noise intensity is adjusted to one or two optimal values, the temporal periodicity of the output of the system reaches the maximum, indicating the occurrence of stochastic resonance (SR) or stochastic bi-resonance (SBR). The resonance behavior is strongly-dependent on the coupling strength in both networks. At a weak coupling, SR more likely takes place; whereas at a strong coupling, SBR is prone to occur. Compared with unweighted networks, the span of coupling strength for SBR is narrower in weighted networks. In addition, the weak signal cannot be amplified so effectively in the weighted networks as in the unweighted networks, attributing to the weakening effect of the link weight on the coupling between oscillators and the heterogeneity of the whole network connectivity caused by the weight distribution.

Stochastic resonance enhancement of small-world neural networks by hybrid synapses and time delay

The synergistic effect of hybrid electrical-chemical synapses and information transmission delay on the stochastic response behavior in small-world neuronal networks is investigated. Numerical results show that, the stochastic response behavior can be regulated by moderate noise intensity to track the rhythm of subthreshold pacemaker, indicating the occurrence of stochastic resonance (SR) in the considered neural system. Inheriting the characteristics of two types of synapses—electrical and chemical ones, neural networks with hybrid electrical-chemical synapses are of great improvement in neuron communication. Particularly, chemical synapses are conducive to increase the network detectability by lowering the resonance noise intensity, while the information is better transmitted through the networks via electrical coupling. Moreover, time delay is able to enhance or destroy the periodic stochastic response behavior intermittently. In the time-delayed small-world neuronal networks, the introduction of electrical synapses can significantly improve the signal detection capability by widening the range of optimal noise intensity for the subthreshold signal, and the efficiency of SR is largely amplified in the case of pure chemical couplings. In addition, the stochastic response behavior is also profoundly influenced by the network topology. Increasing the rewiring probability in pure chemically coupled networks can always enhance the effect of SR, which is slightly influenced by information transmission delay. On the other hand, the capacity of information communication is robust to the network topology within the time-delayed neuronal systems including electrical couplings.

Parameter Tuning in the Application of Stochastic Resonance to Redundant Sensor Systems

<div class=""abs_img""> <img src=""[disp_template_path]/JRM/abst-image/00270003/04.jpg"" width=""340"" />Basic concept of proposed method</div> Stochastic resonance (SR) is a phenomenon by which the addition of random noise improves the detection of weak signals. Thus far, this phenomenon has been extensively studied with the aim of improving sensor sensitivity in various fields of engineering research. However, the possibility of actual application of SR has not been explored because the target signal has to be known in order to confirm the occurrence of SR. In this paper, we propose an optimization method for making SR usable in engineering applications. The underlying mechanism of the proposed method is investigated using information theory and numerical simulation. We developed a tactile sensing system based on the simulation results. The proposed method is applied to this system in order to optimize its parameters for exploiting SR. Results of the experiment show that the developed tactile sensing system successfully achieved higher sensitivity than a conventional system.

Stochastic resonance in visual sensitivity.

It is well known from psychophysical studies that stochastic resonance, in its simplest threshold paradigm, can be used as a tool to measure the detection sensitivity to fine details in noise contaminated stimuli. In the present manuscript, we report simulation studies conducted in the similar threshold paradigm of stochastic resonance. We have estimated the contrast sensitivity in detecting noisy sine-wave stimuli, with varying area and spatial frequency, as a function of noise strength. In all the cases, the measured sensitivity attained a peak at intermediate noise strength, which indicate the occurrence of stochastic resonance. The peak sensitivity exhibited a strong dependence on area and spatial frequency of the stimulus. We show that the peak contrast sensitivity varies with spatial frequency in a nonmonotonic fashion and the qualitative nature of the sensitivity variation is in good agreement with human contrast sensitivity function. We also demonstrate that the peak sensitivity first increases and then saturates with increasing area, and this result is in line with the results of psychophysical experiments. Additionally, we also show that critical area, denoting the saturation of contrast sensitivity, decreases with spatial frequency and the associated maximum contrast sensitivity varies with spatial frequency in a manner that is consistent with the results of psychophysical experiments. In all the studies, the sensitivities were elevated via a nonlinear filtering operation called stochastic resonance. Because of this nonlinear effect, it was not guaranteed that the sensitivities, estimated at each frequency, would be in agreement with the corresponding results of psychophysical experiments; on the contrary, close agreements were observed between our results and the findings of psychophysical investigations. These observations indicate the utility of stochastic resonance in human vision and suggest that this paradigm can be useful in psychophysical studies.

Dynamical complexity and stochastic resonance in a bistable system with time delay

This paper addresses the problem of stochastic resonance (SR) in a time-delayed bistable system subjected to Gaussian white noise. Differing from the conventional studies, the statistical complexity measure and the normalized Shannon entropy have been defined and employed to quantify SR phenomenon of the time-delayed bistable system. According to the definitions of statistical complexity measure and normalized Shannon entropy, a minimum of entropy illustrates that the motion of system reaches some degree of order and a maximum of statistical complexity measure implies that the system’s intricate pattern tends to complexity. It has been found that for an optimal level of noise intensity, the statistical complexity measure displays a maximum and the normalized Shannon entropy exhibits a minimum, which demonstrates not only the occurrence of SR but also the severity of dynamical complexity. And the effects of different parameters on SR are also studied by means of the statistical complexity measure. To test the validity, the signal-to-noise ratio (SNR) is also calculated and a good agreement has been found between the statistical complexity measure and the SNR, which indicates that the statistical complexity measure is an effective method for quantify SR of the time-delayed bistable system.

Stochastic resonance in the Bénard system

In this paper the effect of small stochastic perturbations on a dynamical system describing the Benard thermal convection is studied. In particular, the two-dimensional Oberbeck-Boussinesq equations governing the dynamics of three interacting Rayleigh rolls with increasing horizontal wave numbers (i.e., three horizontal modes in the Fourier transform) are reduced to a system of gradient type. The aim is to study the transition paths between the stable steady states, when a stochastic perturbation is taken into account, and the occurrence of stochastic resonance, when the system is perturbed by white noise and the first (gravest) mode is forced by an external periodic component. Results show that i) random transitions between stable steady states representing a clockwise and a counter-clockwise circulation occur through the two saddle points associated with the second mode and not through the (unstable) conductive state nor the saddle points related to the third mode; ii) the introduction of the third mode, as well as of others of smaller spatial scales, does not affect transitions that remain confined along the trajectories linking stable convective states through the saddle points associated with the second mode; iii) the system exhibits a stochastic resonance behavior leading to large amplification of the small amplitude periodic component compared to the one leading to the classical (one-dimensional) stochastic resonance.

Relative stability of dynamical states and stochastic resonance in a sinusoidal potential

Recently, stochastic resonance was shown to occur in underdamped periodic potentials at frequencies (of the drive field) close to the natural frequency at the minima of the potentials. In these systems the particle trajectories are not arbitrary at low temperatures but follow the drive field with two definite mean phase differences depending on the initial conditions. The trajectories are thus found to be in only two stable dynamical states. The occurrence of stochastic resonance in the periodic potentials was explained as a consequence of the transitions between these two dynamical states as the temperature was increased. In the present work, we find the range of amplitudes of the drive field over which the dynamical states could be observed in a sinusoidal potential. The variation of the relative stability of the dynamical states as a function of drive-field amplitude is clarified by analyzing the nature of curves characterizing the stochastic resonance as the amplitude is varied within the range.

Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise

Stochastic resonance in an underdamped bistable system subjected to a weak asymmetric dichotomous noise is investigated numerically. Dichotomous noise is a non-Gaussian color noise and more complex than Gaussian white noise, whose waiting time complies with the exponential distribution. Utilizing an efficiently numerical algorithm, we acquire the asymmetric dichotomous noise accurately. Then the system responses and the averaged power spectrum as the signatures of the stochastic resonance are calculated by the fourth-order Runge–Kutta algorithm. The effects of the noise strength, the forcing frequency, and the asymmetry of dichotomous noise on the system responses and the effects of the forcing frequency on the averaged power spectrum are discussed, respectively. It is found that the increasing of the noise strength or the forcing frequency could strengthen the passage between the stable points of the system, and the system responses also display the asymmetry for the asymmetric dichotomous noise, which has not been discovered in other investigated results. Additionally, the averaged power spectrum exhibits the sharp peaks, which indicates the occurrence of stochastic resonance, and we also discover two critical forcing frequencies: one denoting the transformation of the peaks and another for the optimum on stochastic resonance.

Periodically driven underdamped periodic and washboard potential systems: Dynamical states and stochastic resonance

We have studied the motion of an underdamped Brownian particle in (i) a bistable periodic potential and (ii) washboard potentials subjected to a sinusoidal external field. The particles are shown to be effectively in two dynamical states of their trajectories with distinct amplitudes and phase relationship with the external drive. These dynamical states are stable with fixed energies at low temperatures, but transitions between them take place as the temperature is increased. The average input energy loss to the environment per period of the drive shows a stochastic resonance (SR) peak as a function of temperature for the underdamped system potentials studied. The occurrence of SR in these systems is explained using the statistics of transitions between the two dynamical states.

Constructive role of noise in p53 regulatory network

We study the effect of noise on p53 regulatory network, the core of a cell's modulator for switching between survival and apoptosis. We find that the fluctuations, originating from stochastic expression of p53-responsive genes, introduce marked advantages for the system to sense external stimuli and sustain the function of switches. The coherence between a stimulus and the system's response undergoes a maximum with the raise of noise level, indicating the occurrence of stochastic resonance. The biological significance of our results is discussed.

Stochastic resonance in bistable confining potentials

We study the effects of the confining conditions on the occurrence of stochastic resonance (SR) in continuous bistable systems. We model such systems by means of double-well potentials that diverge like |x|q for |x|↦∞. For super-harmonic (hard) potentials with q > 2 the SR peak sharpens with increasing q, whereas for sub-harmonic (soft) potentials, q < 2, it gets suppressed.

Nonlinear signal detection from an array of threshold devices for non-Gaussian noise

We discuss the beneficial action of non-Gaussian noise in nonlinear signal detection through an array of threshold devices based on the probability of error. For unimodal generalized Gaussian noise, only when the input signal is sub-threshold, stochastic resonance (SR) exists. The efficacy of SR reduces as the exponent parameter in the noise probability density function (PDF) becomes small. This result is analogical with a previous result where the signal PDF has an effect on the efficacy of SR. The efficacy of SR also reduces as the threshold level is raised. However, for bimodal Gaussian mixture noise, not only when the input signal is sub-threshold, SR sometimes exists, but also when the input signal is supra-threshold, supra-threshold stochastic resonance (SSR) often exists, too. The parameter in the Gaussian mixture noise PDF has an effect on the occurrence of SR and SSR. Array can enhance the efficacy of the nonlinear detection as the number of threshold devices in the array is raised. These results show further that the phenomena of SR and SSR depend on the characteristic of the threshold noise and also extend the applicability of SR and SSR in nonlinear signal detection.

A study on stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point with the moment method

Abstract This paper analyzes the stochastic resonance induced by a novel transition of one-dimensional bistable system in the neighborhood of bifurcation point with the method of moment, which refer to the transition of system motion among a potential well of stable fixed point before bifurcation of original system and double-well potential of two coexisting stable fixed points after original system bifurcation at the presence of internal noise. The results show: the semi-analytical result of stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point may be obtained, and the semi-analytical result is in accord with the one of Monte Carlo simulation qualitatively, the occurrence of stochastic resonance is related to the bifurcation of noisy nonlinear dynamical system moment equations, which induce the transfer of energy of ensemble average (Ex) of system response in each frequency component and make the energy of ensemble average of system response concentrate on the frequency of input signal, stochastic resonance occurs.