Type Of Stochastic Resonance Research Articles

Responses of a Noisy Excitable System to External Signals withDifferent Periods

The behaviour of an excitable system under Gaussian white noiseand external periodic forcing is systematically studied. In alarge range of noise intensity, the n:1 phase locking patterns areobtained for certain ranges of the input periods, where n inputperiods give one spike. In the phase locking regimes, the systempresents low noise-to-signal ratios and shows better regularities.Out of the regimes the system behaves less regularly and therelations between the noise-to-signal ratio and the noiseintensity exhibit typical stochastic resonance phenomena. Ata higher noise level, the system shows the characteristic behaviourof the noise.

Stochastic resonance in a single-mode laser driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts

We present an analytic investigation of the signal-to-noise ratio of output intensity in a loss-noise model of a single-mode laser system driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. Stochastic resonance (SR) in the curve of signal-to-noise ratio R versus the pump noise self-correlation time τ,signal frequency Ω,and cross-correlation coefficient between the real and imaginary parts of the quantum noise λq are found. It extends the conclusion of the typical SR,that is, \!there is a maximum in the curve of R vs noise intensity\". Moreover,we detect that,when the parameter Ω increases,the shape of the Rτ curve will exhibit a change process of multiform SR: the curve experienced from simulta neous existence of resonances and suppressions to single-peak SR and finally to the monotonous rise. And when the parameter τincreases,the shape of theRΩcurve also exhibit a change process of multiform SR: the curve experienced from the monotonous rise to the simultaneous existence of resonances and suppressions and finally to the monotonous descending. For the Rλq curve,it appears an acute single-peak form.

Diffusion in a potential with a time-dependent discontinuity

We investigate the one-dimensional diffusion of a particle in a V-shaped potential combined with a time-dependent jump at the tip. Employing the matching conditions, we calculate the exact Green function of the corresponding Smoluchowski equation. We then specialize the analysis to a harmonically oscillating height of the potential discontinuity. We calculate the particle's mean position as a function of time and study its nonlinear features. Our analysis reveals a new type of stochastic resonance. Namely, the time-asymptotic amplitude of the mean-position oscillations exhibits a maximum at an optimal value of the V-potential slope.

RESONANCE-LIKE PHENOMENA IN ARRAYS OF RÖSSLER OSCILLATORS UNDER CORRELATED PARAMETRIC FLUCTUATIONS

The behavior of diffusively coupled Rössler oscillators parametrically perturbed with an Ornstein–Uhlenbeck noise is analyzed in terms of the degree of synchronization between the cells. A resonance-like behavior is found as a function of the noise correlation time, instead of the noise intensity as it occurs in the typical stochastic resonance. A power law scaling between the "optimum" correlation time with regard to synchronization and the deterministic time scale of the oscillators has been obtained, with an exponent that depends on the coupling strength.

A very stochastic resonant neuron model

We study the properties of a neuron model, the dynamical perceptron, under different stochastic inputs. This model is essentially a discrete time mapping, that can exhibit many neural features like activation threshold and pacemaker behavior, amongst others. Like real neurons, this model can show many different types of stochastic resonance. The addition of white noise causes autonomous stochastic resonance, oscillations with predominance of multiples of some fundamental period. The noise can also enhance subthreshold either periodic ( usual stochastic resonance) or aperiodic ( aperiodic stochastic resonance) external signals.

Nonlinear stochastic resonance: the saga of anomalous output-input gain

We reconsider stochastic resonance (SR) for an overdamped bistable dynamics driven by a harmonic force and Gaussian noise from the viewpoint of the gain behavior, i.e., the signal-to-noise ratio (SNR) at the output divided by that at the input. The primary issue addressed in this work is whether a gain exceeding unity can occur for this archetypal SR model, for subthreshold signals that are beyond the regime of validity of linear response theory: in contrast to nondynamical threshold systems, we find that the nonlinear gain in this conventional SR system exceeds unity only for suprathreshold signals, where SR for the spectral amplification and/or the SNR no longer occurs. Moreover, the gain assumes, at weak to moderate noise strengths, rather small (minimal) values for near-threshold signal amplitudes. The SNR gain generically exhibits a distinctive nonmonotonic behavior versus both the signal amplitude at fixed noise intensity and the noise intensity at fixed signal amplitude. We also test the validity of linear response theory; this approximation is strongly violated for weak noise. At strong noise, however, its validity regime extends well into the large driving regime above threshold. The prominent role of physically realistic noise color is studied for exponentially correlated Gaussian noise of constant intensity scaling and also for constant variance scaling; the latter produces a characteristic, resonancelike gain behavior. The gain for this typical SR setup is further contrasted with the gain behavior for a "soft" potential model.

Nonadiabatic resonances in a noisy Fitzhugh-Nagumo neuron model

We have analyzed the response of a noisy Fitzhugh-Nagumo neuronlike model (FN) to subthreshold external stimuli. In contrast to previous studies we have focused our attention on high-frequency signals which could be of interest for real systems such as nervous fibers in the auditory system. We show that the noisy FN behaves as a stochastic oscillator with a characteristic time scale whose effects remain in a wide range of situations. In the nonadiabatic regime of frequencies considered in this work we report several resonant behaviors which resemble those of classical deterministic oscillators but never the typical stochastic resonance phenomenon so often observed for low-frequency signals.

Cooperative behavior in the Fitzhugh–Nagumo neuron: Consequences for acoustic perception

Recent studies have shown that a type of stochastic resonance, known as cooperative behavior, can occur in biological neurons. This behavior is characterized by phase locking between the pulse position modulation of the neuron’s activation and weak sinusoidal input signals. The behavior is strongly influenced by the level of background noise in the system. Significantly, it is common for the phase of the neuron activation to lock on a subharmonic of any sinusoidal input stimulation or on subharmonics of a combination of tones. If the Fitzhugh–Nagumo neuron is simulated as an integrate-and-fire (Wiener) process, it can be shown that a single neuron demonstrates cooperative behavior modes which correspond to the known phenomena of acoustic perception (if the neural input is assumed to be a sonic stimulus). Most significantly, the perception of virtual pitch is apparent, as is the pitch shift effect. When presented with an amplitude modulated waveform, the neuron locks on peak features of the time representation of the waveform, thereby recreating the effects discovered by Schouten [Philips Tech. Rev. 5, 286–301 (1940)]. It seems likely that this simple model explains some of the physiological bases for the nature of pitch perception.

Cortical Synchronization and Perceptual Framing

How does the brain group together different parts of an object into a coherent visual object representation? Different parts of an object may be processed by the brain at different rates and may thus become desynchronized. Perceptual framing is a process that resynchronizes cortical activities corresponding to the same retinal object. A neural network model is presented that is able to rapidly resynchronize desynchronized neural activities. The model provides a link between perceptual and brain data. Model properties quantitatively simulate perceptual framing data, including psychophysical data about temporal order judgments and the reduction of threshold contrast as a function of stimulus length. Such a model has earlier been used to explain data about illusory contour formation, texture segregation, shape-from-shading, 3-D vision, and cortical receptive fields. The model hereby shows how many data may be understood as manifestations of a cortical grouping process that can rapidly resynchronize image parts that belong together in visual object representations. The model exhibits better synchronization in the presence of noise than without noise, a type of stochastic resonance, and synchronizes robustly when cells that represent different stimulus orientations compete. These properties arise when fast long-range cooperation and slow short-range competition interact via nonlinear feedback interactions with cells that obey shunting equations.

Validity of basic concepts in nonlinear cooperative Fokker-Planck models.

The stochastic amplification of a periodic signal in a truly nonlinear Fokker-Planck model, whose drift coefficient exhibits a functional dependence on the distribution function, is analyzed numerically by means of a finite-difference method. Our aim is to check the validity of basic concepts widely used in studying linear and/or undriven systems. A perturbation approach to numerically evaluate the generalized susceptibility of the model by means of the linear response theory is tested and found to be adequate for weak driving fields. We also check the validity of the Floquet theory and the H theorem for which no extension to the case of truly nonlinear driven systems exists. The influence of the functional nonlinearity on the typical stochastic resonance effects is pointed out. \textcopyright{} 1996 The American Physical Society.

Stochastic Resonance with Sensitive Frequency Dependence in Globally Coupled Continuous Systems

A model of globally coupled bistable continuous systems with two series of cells, modeling competing processes between activators and suppressors, subject to periodic and stochastic forces is investigated. In the large system size limit the exact solution of linear response theory is obtained, which shows typical stochastic resonance (SR) behavior. In particular, we find a resonance, sensitively depending not only on noise intensity and coupling strength, but also on the frequency of the periodic forcing. The SR occurs at a noise-induced Hopf bifurcation point, and is associated with the divergence of linear response.

Langevin description of the response of a stochastic mean-field model driven by a time-periodic field.

We analyze the dynamical response of a nonlinear stochastic model with mean-field coupling driven by a time-sinusoidal external field. The Langevin equation for the model is solved numerically, and the results indicate the possibility of observing stochastic resonant amplification of the driving amplitude. The influence of the mean-field coupling on the typical stochastic resonance effects is pointed out.

Nonconventional stochastic resonance

It is argued, on the basis of linear response theory (LRT), that new types of stochastic resonance (SR) are to be anticipated in diverse systems, quite different from the one most commonly studied to date, which has a static double-well potential and is driven by a net force equal to the sum of periodic and stochastic terms. On this basis, three new nonconventional forms of SR are predicted, sought, found, and investigated both theoretically and by analogue electronic experiment: (a) in monostable systems; (b) in bistable systems with periodically modulated noise; and (c) in a system with coexisting periodic attractors. In each case, it is shown that LRT can provide a good quantitative description of the experimental results for sufficiently weak driving fields. It is concluded that SR is a much more general phenomenon than has hitherto been appreciated.