Stochastic Resonance Behavior Research Articles

The influence of potential to stochastic resonance in model system of bistable states chemical reaction

The dynamics of modified Schlögl model in a continuous-flow-stirred-tank reactor system was investigated numerically. The stochastic resonance behavior was observed in this bistable system. However, the signal-noise-ratio was found to be proportional to the height of potential barrier.

Dynamic transition and resonance in current-driven arrays of Josephson junctions

We consider a two-dimensional fully frustrated Josephson-junction array, which is driven uniformly by oscillating currents. As the temperature is lowered, there emerges a dynamic phase transition to an ordered state with a nonzero dynamic order parameter for small currents. The transition temperature decreases monotonically with the driving amplitude, approaching zero at a certain critical value of the amplitude. Above the critical value, the disordered phase and the dynamically ordered phase are observed to appear alternatively. The characteristic stochastic resonance behavior of the system is also examined, which reveals that the resonance behavior of odd and even harmonics can be different according to the zero-temperature state.

Pattern formation of spiral waves in an inhomogeneous medium with small-world connections.

Pattern formation of spiral waves in an inhomogeneous excitable medium with small-world connections is investigated. In both cases, with completely local regular connections and with completely random connections, spiral waves cannot survive in the given inhomogeneous medium. It is found that with small-world connections (basically local connections plus a small number of random connections) a well behaved spiral wave can be formed against the destructive role of the inhomogeneous medium. There also exists an optimal fraction of random connections which can greatly enhance the probability of spiral wave formation; this resembles the behavior of stochastic resonance.

Stochastic resonance in human electroencephalographic activity elicited by mechanical tactile stimuli

Stochastic resonance (SR) is a phenomenon in which the response of a non-linear system to a weak input signal is optimized by the presence of noise. The aim of this study was to demonstrate the experimental occurrence of SR in electroencephalographic (EEG) activity elicited by mechanical tactile stimuli. Our experiments show that EEG responses evoked by mechanical tactile stimuli in the region overlying the somatosensory cortical area were optimized by the addition of certain noise amplitudes. All subjects showed distinct SR behavior. The signal-to-noise ratio (SNR) of the response evoked by mechanical indentations of the skin was an inverted U-like function of the input noise. As the noise amplitude increased, SNR values became larger. A maximum value was reached with a particular noise amplitude value. Beyond such peak, with higher noise amplitudes, the curve subsided gradually. To our knowledge, this is the first documented evidence that such remarkable phenomenon embodies electrical processes of the human brain. Such behavior might explain related findings described in psychophysical studies.

Noise-enhanced temporal association in neural networks.

We consider a network of globally coupled neuronal oscillators subject to random force, and investigate numerically dynamic responses to external periodic driving. The order parameter, which measures the overlap between the configuration of the system and embedded patterns, is found to exhibit stochastic resonance behavior, as manifested by the signal-to-noise ratio (SNR). The optimal noise level at which the SNR reaches its maximum is found to depend on the driving frequency. On the other hand, as the randomness in the driving amplitude is increased, the system undergoes a transition from the memory-retrieval state to the mixed-memory one. The noise effects on the temporal-association state in the absence of external periodic driving are also investigated, revealing similar noise-enhanced resonance.

Stochastic resonance in delayed two-coupled oscillators with input signals different in frequency

Stochastic resonance (SR) is investigated in a two-coupled oscillator system with time delay and a pinning force. Each oscillator is driven by a periodic signal and Gaussian white noise. Periodic signals at their inputs have equal amplitude but different frequencies. We find that each oscillator's SR behavior, which is described by the change of the signal-to-noise ratio (SNR) at the frequency of the signal into itself against the noise intensity, is in good agreement with that of the corresponding uncoupled single oscillator. In addition, the output SNR of one oscillator at the frequency of the signal into the other oscillator also demonstrates SR-like behavior with the increment of noise intensity. The results indicate the coexistence of decoupling and coupling effects and have implications in the area of information transmission in coupled-element neural network.

Spike timing precision for a neuronal array with periodic signal

The spike timing precisions of an array of neurons to periodic input are studied. For weak signal, the precision versus the noise intensity shows a stochastic resonance (SR) behavior. The optimal noise intensity corresponding to the maximal resonance shows a global minimum as increasing signal frequency. As the signal amplitude increases above a critical value, the SR effect disappears, and the critical amplitude goes through a global minimum as the signal frequency increases. A frequency sensitive range of 30–100 Hz with high spike timing precisions and high coherence of the firings are found. It is the resonance between the intrinsic oscillation and the signal resulting in the dependence of the dynamical features of SR on the forcing frequency and the frequency sensitivity.

Simple electronic circuit model for doubly stochastic resonance.

We have recently reported the phenomenon of doubly stochastic resonance [Phys. Rev. Lett. 85, 227 (2000)], a synthesis of noise-induced transition and stochastic resonance. The essential feature of this phenomenon is that multiplicative noise induces a bimodality and additive noise causes stochastic resonance behavior in the induced structure. In the present paper we outline possible applications of this effect and design a simple lattice of electronic circuits for the experimental realization of doubly stochastic resonance.

Stochastic resonance and nonlinear response using NMR spectroscopy

We revisit the phenomenon of quantum stochastic resonance in the regime of validity of the Bloch equations. We find that a stochastic resonance behavior in the steady-state response of the system is present whenever the noise-induced relaxation dynamics can be characterized via a single relaxation time scale. The picture is validated by a simple nuclear magnetic resonance experiment on water.

Stochastic resonance in ion channels characterized by information theory.

We identify a unifying measure for stochastic resonance (SR) in voltage dependent ion channels which comprises periodic (conventional), aperiodic, and nonstationary SR. Within a simplest setting, the gating dynamics is governed by two-state conductance fluctuations, which switch at random time points between two values. The corresponding continuous time point process is analyzed by virtue of information theory. In pursuing this goal we evaluate for our dynamics the tau information, the mutual information, and the rate of information gain. As a main result we find an analytical formula for the rate of information gain that solely involves the probability of the two channel states and their noise averaged rates. For small voltage signals it simplifies to a handy expression. Our findings are applied to study SR in a potassium channel. We find that SR occurs only when the closed state is predominantly dwelled upon. Upon increasing the probability for the open channel state the application of an extra dose of noise monotonically deteriorates the rate of information gain, i.e., no SR behavior occurs.

Periodic and random perturbation of catalytic oxidation of CO

When a controllable input is modulated by noise and signal, the response of a nonlinear system may exhibit a synchronized effect, which is referred to as stochastic resonance(SR). With the help of noise, the detection of weak signal may become possible and its signal-to-noise ratio can be increased. A model to describe catalytic oxidation of CO on single crystal was adopted, and its stability was studied by linear analysis method. Through computer simulation, the responses under periodic and random perturbation were analyzed. Stochastic resonance behavior was found in a narrow bistable region, or near the oscillatory region. The results shows more characteristics than those of 1-dimensional system does.

Stochastic resonance in the absence and presence of external signals for a chemical reaction

A catalytic reduction of NO with CO on Pt(100) surface is adopted to study its response under random perturbation. Noise-induced oscillations and noise-induced frequency shifts have been observed when the system works in the vicinity of the oscillatory region and meanwhile is subjected to random modulation of its feeding speed. Stochastic resonance behavior can be recognized from the noise-induced peak in the power spectrum even though in the absence of external signals. The numerical results have been obtained near supercritical Hopf bifurcation points, but are not confined to the classification of bifurcation. When the system falls into bistable regions, noise can help an external weak signal to induce state-to-state transitions and also shows a stochastic resonance behavior except for the case that the system has an isolated bifurcation scheme.

Noise-enhanced transmission of information in a bistable system

Stochastic resonance (SR) in a bistable system with a binary input signal is studied by numerical simulation. The mutual information (MI) is used as a measure of information. We show that MI shows the resonance peculiar to SR and that the output MI of the bistable system can exceed the input one, that is, MI can have gain. The dependence of the resonance signal and the gain of MI on the noise cutoff frequency is studied and it is shown that the noise with large cutoff frequency is favorable for SR and for the gain of MI. To show the characteristics and the benefits of this type of SR and the gain of MI, the behavior of SR in the bistable system for image data is simulated. The simulation results show that this system can improve the visibility of images.

Signal transmission in one-way coupled bistable systems: Noise effect

Signal transmission in a nonlinear medium described by one-way coupled bistable systems subject to uncorrelated noise is investigated. It is found that noise can play an active role to effectively improve the signal transmission. Stochastic resonance behavior can appear in the signal transmission process, and at the optimal noise intensity one can find the largest output signal amplitude and the largest signal transmission distance. In particular, in certain cases undamped signal transmission can be stimulated by the combined action of both injected signal and noise, while the signal damps exponentially with space distance without noise.

Stochastic resonance in surface catalytic oxidation of carbon monoxide

Stochastic resonance is a nonlinear cooperative effect between external signal and noise, in which the noise can play a constructive role to increase the signal-to-noise ratio in the detection of a weak signal. A surface catalytic reaction model, to describe oxidization of carbon monoxide carrying out far from equilibrium, was adopted to study the stochastic resonance. By computer simulation, we found noise can induce state-to-state transitions, and stochastic resonance behavior may appear at narrow bistable states or near discontinuous Hopf bifurcations, while a weak periodic signal riding on noise is input controlling.

Stochastic resonance and cooperative behavior in scanning probe microscopy

Stochastic resonance and cooperative behavior in scanning probe microscopy

Stochastic resonance in a mode locked acoustic interferometer

Stochastic resonance (SR) refers to a cooperative non-linear coupling of weak signals and noise, in systems whose signal response consists of transitions from one state to another. It has not previously been identified in an acoustic or ultrasonic system. In this paper, we examine SR behaviour in a mode-locked ultrasonic interferometer, and show that the classic signatures of the phenomenon are present. The coupling of energy can be used to improve the signal-to-noise ratio of the system and, in addition, provides some insight into the SR phenomenon itself.

Dynamical Hysteresis and Stochastic Resonance in Driven Dissipative Quantum Two-State System

We study the dynamics of a periodically driven two-state system coupled to thermal environment. In the high temperature limit we have obtained analytic expressions for the average position of the particle and hysteresis loop area. Both these quantities exhibit stochastic resonance behavior as a function of various parameters of the problem. These two resonances, however, occur at different values of the parameters. The resonance condition obtained from the study of phase delay exhibits resonance at a fixed frequency independent of other physical parameters.

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.

Nonlinear-response effects in stochastic resonance.

Nonlinear-response effects in stochastic resonance are investigated. An analytic solution is obtained in the framework of the adiabatic approximation. It is found that the input signal strength plays an important role in affecting the stochastic resonance behavior. Our analytic predictions fit well both numerical calculations and experimental results