Frequency adaptation in controlled stochastic resonance utilizing delayed feedback method: Two-pole approximation for response function

In this paper, (supra-threshold) stochastic resonance phenomenon of noise-enhanced information transmission is studied in detail through the numerical calculation and the computer simulation in a non-linear multilevel threshold neural networks system, which is affected by both additive noise and multiplicative noise, then the mutual information is used to characterize the phenomenon. The mutual information as a function of additive noise intensity or multiplicative noise intensity brings on convex changes under a suitable system threshold and a fixed multiplicative noise intensity or additive noise intensity, which shows that the (supra-threshold) stochastic resonance phenomenon occurs. The increases in the number of the system threshold units can enhance the effectiveness of information transmission; the increase of the system threshold can increase the signal components that are under the threshold, and thus the supra-threshold stochastic resonance takes place more easily. In addition, by changing the additive noise intensity the supra-threshold stochastic resonance occurs more easily than by changing the multiplicative noise intensity. The above results show that both the existence of the supra-threshold stochastic resonance and the effectiveness of noise-improved the signal transmission are closely related to multiplicative or additive noise intensity, the number of threshold units, and the system threshold level.

Effects of multiscale noise tuning on stochastic resonance for weak signal detection

The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

Stochastic resonance(SR) in a FitzHugh-Nagumo neuron model is investigated based on a dynamic mutual information (DMI) between the input and the corresponding output signals. The DMI is expressed in terms of the (cross)power spectra of the input and output time series. Both stochastic-periodic and aperiodic SR are treated based on the DMI and our results are in good accord with the SR measured by the signal to noise ratio(SNR) for the case of the stochastic-periodic input and the power norm for the case of the aperiodic input.

Stochastic resonance (SR) is one of the basic principles intrinsically possessed by any living thing to highly adapt to complicated environments including various disturbances. Although a noise is inevitably mixed by contact with an object and a sensor's movement on it in tactile sensing, a human being can evaluate the several micrometers of unevenness on the object surface by means of SR. We intend to apply SR to tactile sensing and to develop a tactile sensing system capable of measuring an object surface with high precision in not only a controlled environment like a precision measurement room but also in a living environment. First, we investigate the SR characteristic possessed by a Hodgkin-Huxley model, which can emulate a squid's neuron activities. According to the simulation results, we develop a new electronic circuit capable of generating the SR. We perform the object surface scan using a linear robot equipped with a tactile sensor and the circuit. A series of object surface scanning tests is repeated while changing the intensity of applied noise and compute the signal to noise ratio (SNR, hereafter) from the obtained measurement data to check the effect of the SR. In the experiment, stripe-shaped textures with a height of δ=5-30 μm are used as specimens. The SNR changes depending on the noise intensity, and the local maximum appears under a proper noise. It is found that sensing accuracy is improved according to the aforementioned SR theory. Therefore, SR, which is usually applied to noisy environments, is effective for a tactile sensing system.

Stochastic resonance is a noise phenomenon that benefits applications such as pattern formation, neural systems, microelectromechanical systems, and image processing. This study experimentally clarifies that the orientation of the liquid crystal molecules was switched between two stable positions when stochastic resonance was induced by colored noises in a liquid crystal light valve with optical feedback. Ornstein-Uhlenbeck and dichotomous noises were used for colored noise, and the noise was applied to the drive voltage of the liquid crystal light valve. The signal-to-noise ratio was measured with respect to changes in the noise type, noise intensity, and autocorrelation time of the noise. It was found that typical stochastic resonance was observed with a noise autocorrelation time of approximately 20 ms or more for both noise types, and dichotomous noise further enhanced the stochastic resonance compared to the Ornstein-Uhlenbeck noise. This suggests that it is possible to maximize stochastic resonance in a liquid crystal light valve by optimizing the conditions of colored noise.

The analysis of a birhythmic modified van der Pol type oscillator driven by periodic excitation and Lévy noise shows the possible occurrence of coherence resonance and stochastic resonance. The frequency of the harmonic excitation in the neighborhood of one of the limit cycles influences the coherence of the dynamics on the time scale of the oscillations. The autocorrelation function, the power spectral density and the signal-to-noise-ratio used in this analysis are shown to be maximized for an appropriate choice of the noise intensity. In particular, a proper adjustment of the Lévy noise intensity enhances the output power spectrum of the system, that is, promotes stochastic resonance. Thus, the resonance, as examined using standard measures, seems to occur also in the presence of nonstandard noise. The initial selection of the attractor seems to have an influence on the coherence, while the skewness parameter of the Lévy noise has not a notable impact on the resonant effect.

Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise

A recent analysis of the energy detector model in sensory psychophysics concluded that stochastic resonance does not occur in a measure of signal detectability ( d'), but can occur in a percent-correct measure of performance as an epiphenomenon of nonoptimal criterion placement [Tougaard (2000) Biol Cybern 83: 471-480]. When generalized to signal detection in sensory systems in general, this conclusion is a serious challenge to the idea that stochastic resonance could play a significant role in sensory processing in humans and other animals. It also seems to be inconsistent with recent demonstrations of stochastic resonance in sensory systems of both nonhuman animals and humans using measures of system performance such as signal-to-noise ratio of power spectral densities and percent-correct detections in a two-interval forced-choice paradigm, both closely related to d'. In this paper we address this apparent dilemma by discussing several models of how stochastic resonance can arise in signal detection systems, including especially those that implement a "soft threshold" at the input transform stage. One example involves redefining d' for energy increments in terms of parameters of the spike-count distribution of FitzHugh-Nagumo neurons. Another involves a Poisson spike generator that receives an exponentially transformed noisy periodic signal. In this case it can be shown that the signal-to-noise ratio of the power spectral density at the signal frequency, which exhibits stochastic resonance, is proportional to d'. Finally, a variant of d' is shown to exhibit stochastic resonance when calculated directly from the distributions of power spectral densities at the signal frequency resulting from transformation of noise alone and a noisy signal by a sufficiently steep nonlinear response function. All of these examples, and others from the literature, imply that stochastic resonance is more than an epiphenomenon, although significant limitations to the extent to which adding noise can aid detection do exist.

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.

In this paper, mean first-passage time (MFPT) and stochastic resonance (SR) are investigated in an asymmetric bistable system driven by multiplicative non-Gaussian noise and additive Gaussian white noise. Using the path integral approach and two-state theory, the expression of MFPT and the signal-to-noise ratio (SNR) are derived. The results show that the influences of the asymmetric coefficient on the MFPTs in two opposite directions are entirely different. SNR is a non-monotonic function of the additive noise intensity and asymmetric coefficient, therefore, an SR is found in this system. Whereas SNR is a monotonic function of the multiplicative noise intensity and no SR appears. This demonstrates that the effect of the multiplicative noise intensity on SNR is different from that of the additive noise intensity in the system.

A deterministic periodic signal plus a stationary random noise is applied to a static nonlinearity taking the form of a monovariable arbitrary function on real numbers. The property of noise-enhanced signal transmission through stochastic resonance is studied for this class of static nonlinear systems. A theory is developed that provides expressions for the output autocorrelation function, power spectral density, signal-to-noise ratio, and input-output phase shift, in the presence of a periodic input, a noise distribution, and a static nonlinearity, all three being arbitrary. Both white and colored input noises are successively considered. For white input noise, exact expressions are derived in a discrete-time framework directly confrontable to simulations or experiments. The theory is applied to describe stochastic resonance in various examples of static nonlinear systems, for instance, a diode nonlinearity. In addition, confrontations with experiments and simulations are given that support the theory. In particular, interesting effects are reported such as a signal-to-noise ratio larger at the output than at the input or stochastic resonance at zero frequency. Finally, the validity of the theory is extended to dynamic nonlinear systems that can be decomposed into a static nonlinearity followed by an arbitrary dynamic linear system. @S1063-651X~97!12002-5#

The effect of stochastic resonance is investigated. The principles of the effect are considered on the basis of a Brownian particle moving in a system with a symmetric bistable potential. Different from the widely existing noise elimination methods, stochastic resonance enables a new method to utilize the energy of noises, nonlinear system, and signal frequency to reach certain weak signal enhancement effects that noise elimination cannot perform well. The presence of noise at the input of nonlinear systems possessing the effect of the stochastic resonance allows to stand out a weak signal from an additive mixture with white Gaussian noise. The equation and structural scheme of stochastic resonance are considered The conditions for the occurrence of stochastic resonance are formulated and the determining role of noise variance in the realization of this effect is shown. For the first time, a numerical calculation of standing out of harmonic oscillation from an additive mixture with white Gaussian noise based on the stochastic resonance effect is carried out. The output signal-to-noise ratio dependence of the stochastic resonator on the intensity of input noise and the input signal frequency is investigated. The frequency dependencies of the output signal are investigated and the components of this signal are analysed. It is shown that the stochastic resonator acts as a low-pass filter and reduces the output noise level. Numerical modelling of the stochastic resonance effect also shows that the output signal of the stochastic resonator contains odd harmonics of the input oscillation, which is characteristic of nonlinear systems. It is shown that the stochastic resonance effect can be widely used in radio engineering and telecommunications to amplify the useful signal.

Frequency dependent stochastic resonance in a model for intracellular Ca 2+ oscillations can be explained by local divergence

Stochastic resonance (SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density (SPD) and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations (MCS) confirm the effectiveness of the theoretical results.