Stochastic Resonance Effect Research Articles

Oscillatory amplification of stochastic resonance in excitable systems.

We study systems which combine both oscillatory and excitable properties, and hence intrinsically possess two internal frequencies, responsible for standard spiking and for small amplitude oscillatory limit cycles (Canard orbits). We show that in such a system the effect of stochastic resonance can be amplified by application of an additional high-frequency signal, which is in resonance with the oscillatory frequency. It is important that for this amplification one needs much lower noise intensities as for conventional stochastic resonance in excitable systems.

Stochastic resonance in noisy threshold neurons

Stochastic resonance occurs when noise improves how a nonlinear system performs. This paper presents two general stochastic-resonance theorems for threshold neurons that process noisy Bernoulli input sequences. The performance measure is Shannon mutual information. The theorems show that small amounts of independent additive noise can increase the mutual information of threshold neurons if the neurons detect subthreshold signals. The first theorem shows that this stochastic-resonance effect holds for all finite-variance noise probability density functions that obey a simple mean constraint that the user can control. A corollary shows that this stochastic-resonance effect occurs for the important family of (right-sided) gamma noise. The second theorem shows that this effect holds for all infinite-variance noise types in the broad family of stable distributions. Stable bell curves can model extremely impulsive noise environments. So the second theorem shows that this stochastic-resonance effect is robust against violent fluctuations in the additive noise process.

Injection locking near a stochastic bifurcation: the dc SQUID as a case study

We examine the response of a 2D nonlinear oscillator (exemplified in this work by the two-junction superconducting quantum interference device - SQUID) subject to a weak time-periodic target signal, just past the onset of a saddle-node bifurcation. Adjusting the control parameters of the device allows us to identify a regime wherein the response (characterized by an output signal-to-noise ratio at the target frequency) is maximal. The phenomenon has the flavor of the well-studied stochastic resonance effect but is, in fact, shown to arise from a nonlinear deterministic resonance in the “running solution” regime. Our results are presented in the context of experimental results.

Effects of some sorts of nonlinear systems on signal processing via parameter optimized stochastic resonance

This paper deals with the effects of stochastic resonance in some sorts of nonlinear dynamic systems on multi-frequency signal processing in the presence of white or colored noise. By means of tuning system parameters and changing the nonlinear systems, the ability of the systems driven by noise to process a weak signal can be enhanced. We are trying to look for a more effective system to process signals and to find a few systems which have higher effectiveness on signal processing in some circumstances. The numerical simulations strongly support the theoretical conclusions.

ON LOGARITHMIC ASYMPTOTICS OF STOCHASTIC RESONANCE FREQUENCIES

Stochastic resonance effects due to arbitrarily small amplitude deterministic perturbations in dynamical systems with noise are studied. The concept of Log-Asymptotic Resonance Frequency is introduced and the relationship between its existence and some types of symmetries in the stochastic system is established; the spectrum of this kind of frequencies is determined. These symmetries are defined through the quasi-deterministic approximation of the system. The large deviation theory gives the basic machinery for this analysis.

Stochastic phase synchronization in the crayfish mechanoreceptor/photoreceptor system.

The two light-sensitive neurons in the crayfish's abdominal sixth ganglion ("caudal photoreceptors," or CPRs), are both primary light sensors and secondary neurons in a mechanosensory pathway. Pei et al. (1996) demonstrated that light enhances the transduction of weak, periodic hydrodynamic stimuli (measured as an increase in the signal-to-noise ratio at the stimulus frequency in the power spectrum of the recorded neural spikes). This has been interpreted as a stochastic resonance effect, in which added light increases the noise intensity of the input to the photoreceptor (possibly through fluctuations in membrane potential), leading to an enhancement of the signal-to-noise ratio (SNR). Here, we discuss the recent demonstration (Bahar et al., 2002) of the correlation between a stochastic-resonance-like effect and an increase in stochastic phase synchronization between the neural response and a periodic mechanical stimulus. We also discuss a novel effect (Bahar et al., 2002) in which light increases the SNR of the second higher harmonic of a periodic input signal, effectively rectifying the input signal. This "second harmonic effect" can also be interpreted in terms of stochastic phase synchronization (Bahar et al., 2002). We review other recent results on the role of stochastic phase synchronization in mediating sensory responses in the crayfish nervous system.

Stochastic resonance for an optimal detector with phase noise

A stochastic resonance effect, under the form of a noise-improved performance, is shown possible for an optimal detector. This is established with a nonlinear signal–noise mixture where the noise acts on the phase of a periodic signal. The optimal detector, achieving minimal probability of detection error, is explicitly derived. Conditions are exhibited where this minimal probability of error is reduced when the noise level is raised. These results contribute a new step in the investigation of stochastic resonance and in the inventory of its potentialities for nonlinear signal processing.

Stochastic Resonance and Domain Switching

Triglycine sulfate (TGS) is the first ferroelectric material that has been reported to exhibit the effect of stochastic resonance. We observed the effect experimentally, varying the noise strength added to a periodic signal, that was too weak to cause switching between the two possible states of polarization in ferroelectric TGS. Despite the fact that most of the theoretical predictions could be confirmed in our experiments, there occured some peculiarities that have not been observed in other systems with stochastic resonance. The most obvious effect is the dependence of the spectral amplification and the signal-to-noise-ratio on the direction of noise variation. It can be explained taking into account the mechanism of domain switching in ferroelectric materials.

Oscillations in thе distributed system of interacting backward waves at the presence of fluctuations

Both periodic and chaotic oscillations are studied numerically in the distributed dynamic system with interacting of backward linear and nonlinear waves at the presence of additive noise in nonlinear wave. Studied distributed system is the simplest model of the electronic backward wave oscillators with non-inertial bunching mechanisms. It is shown, that excitation of а lot оf space modes is typical for such systems. It is found, that spectrum оf chaotic oscillation near their excitation threshold is very non-uniform. In this case an external noise is «superimposed» on self-sustained oscillations. In the mode of chaotic oscillations at high-current beam under the external noise influence, it may be both increase of chaos and regulating of generated signal form, exhibiting the properties inherent in effect of stochastic resonance.

Stochastic resonance in a superparamagnetic particle

The stochastic resonance (SR) effect in a single-domain particle is investigated for the case where the exciting field is imposed not parallel to the anisotropy axis but at an arbitrary angle. We show that despite the fact that for the transverse case there is no SR at all, the intermediate cases yield signal-to-noise ratios much higher than the well-investigated longitudinal case. The frequency range over which the effect is observable is estimated.

Stochastic resonance as a model for financial market crashes and bubbles

A bistable model of a financial market is considered, aimed at modelling financial crashes and bubbles, based on the Ising model with thermal-bath dynamics and long-range interactions, subject to a weak external information-carrying signal and noise. In the ordered phase, opposite stable orientations of magnetization correspond to the growing and declining market before and after the crash or bubble, and jumps of magnetization direction correspond to crashes and bubbles. It is shown that the influence of an information-carrying signal, assumed to be too weak to induce magnetization jumps, can be enhanced by the external noise via the effect of stochastic resonance. It is argued that in real stock markets the arrival of a piece of information, considered a posteriori to be the cause for a crash or bubble, can be enhanced in a similar way, thus leading to price return whose value is unexpectedly large in comparison with relatively weak importance of this piece of information.

Signal detection theory, detectability and stochastic resonance effects.

Stochastic resonance is a phenomenon in which the performance of certain non-linear detectors can be enhanced by the addition of appropriate levels of random noise. Signal detection theory offers a powerful tool for analysing this type of system, through an ability to separate detection processes into reception and classification, with the former generally being linear and the latter always non-linear. Through appropriate measures of signal detectability it is possible to decide whether a local improvement in detection via stochastic resonance occurs due to the non-linear effects of the classification process. In this case, improvement of detection through the addition of noise can never improve detection beyond that of a corresponding adaptive system. Signal detection and stochastic resonance is investigated in several integrate-and-fire neuron models. It is demonstrated that the stochastic resonance observed in spiking models is caused by non-linear properties of the spike-generation process itself. The true detectability of the signal, as seen by the receiver part of the spiking neuron (the integrator part), decreases monotonically with input noise level for all signal and noise intensities.

Phase synchronization and stochastic resonance effects in the crayfish caudal photoreceptor.

We study the nonlinear response of the crayfish caudal photoreceptor to periodic mechanical stimuli in terms of stochastic synchronization. The amplitude and frequency of the mechanical stimuli and the light level are used as control parameters. The system shows multiple locking regions as the stimulus frequency is varied. We find that the synchronization index increases as the signal-to-noise ratio (SNR) of the periodic drive, in response to increasing light levels; this effect exhibits features similar to stochastic resonance. We demonstrate a nonlinear rectification effect in which the SNR of the second harmonic of the input stimulus increases as the light level is raised, and show that the corresponding synchronization index increases as the SNR of the second harmonic.

Adjusting stochastic resonance in a leaky integrate and fire neuron to sub-threshold stimulus distributions

Here we study in an abstract model how a single neuron could adapt its properties to maximize information processing capabilities in case of weak signal input and additional noise, the natural realm of stochastic resonance. The dynamics of the membrane potential is described by an Ornstein–Uhlenbeck process in a hazard function approximation. First we analytically and numerically characterize the effect of stochastic resonance as a function of the model's parameters. Then we derive an activity-dependent learning rule for the adjustment of the noise inputs and show that it only depends on quantities which could be estimated locally by the neuron.

Stochastic resonance-based input circuits for SQUIDs

A model is reported of a novel frequency-tuneable superconductive amplifier based on stochastic resonance effect in 4-terminal SQUID. The model considers a controllable bistable oscillator with the potential barrier separating two metastable states of superconducting ring closed by a 4-terminal mesoscopic weak link. The barrier is governed by the transport current driven through the other two leads of the 4-terminal weak link. Numeric simulations show the stochastic resonance regime is achieved if some external noise and small sine signal are applied. The signal gain and frequency properties strongly depend then on the transport current. In addition, the stochastic-like resonance is observed when the SQUID is affected by a sine high-frequency signal instead of the white noise pumping.

Stochastic Resonance in a Coupled Array Without Periodic Driving

We manifest a stochastic resonance in a two-dimensional square arrayof coupled oscillators subjected only to white noise andconstant driving forces. The result shows that the coherent outputof every single oscillator plays the role of periodicinput to its neighbours. Even without periodic driving,the cooperation of the white noise and the coupling canalso result in the array enhanced stochastic resonance effect. In ourinvestigation, global as well as local noise perturbationis taken into account.

Stochastic resonance in a thermokinetic reaction system

We present numerical simulations of the counterintuitive effect of stochastic resonance in a model of a thermokinetic chemical oscillator. Small periodic perturbations are amplified by stochastic or deterministically chaotic parameter fluctuations giving way to large temperature oscillations. Stochastic resonance is characterized by various means, among them Fourier transforms, probability distribution functions and interspike histograms.

Generic noise-enhanced coding in neuronal arrays.

We demonstrate that, in a parallel array of model neurons, the optimizing influence of internal noise on the global information is far greater than that reported for a single neuron. In particular, stochastic resonance (SR) effects, that optimize information transmission, occur independent of stimulus level or the setting of the neural threshold. We further show that adjusting the threshold to maximize information transmission does not remove SR effects. Consequently, and in contrast to a single neuron, in neuronal arrays noise appears to be an essential element of an optimal coding strategy.

Multifractal characterization of stochastic resonance.

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force, singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.

Suprathreshold stochastic resonance: an exact result for uniformly distributed signal and noise

An exact analytical expression for the information transmitted through an array of threshold elements subject to a uniformly distributed signal and internal noise is presented. Additionally, approximations that accurately predict the optimal noise intensity and information gains achieved by the recently reported effect of suprathreshold stochastic resonance (N.G. Stocks, Phys. Rev. Lett. 84 (2000) 2310) are obtained.