Presence Of Stochastic Resonance Research Articles

Collective Behaviors of Star-Coupled Harmonic Oscillators with Fluctuating Frequency in the Presence of Stochastic Resonance

The stochastic resonance (SR) of a star-coupled harmonic oscillator subject to multiplicative fluctuation and periodic force in viscous media is studied. The multiplicative noise is modeled as a dichotomous noise and the memory of viscous media is characterized by a fractional power kernel function. By using the Shapiro–Loginov formula and Laplace transform, we obtain the analytical expressions of the first moment of the steady-state response and study the relationship between the system response and the system parameters in the long-time limit. The simulation results show the nonmonotonic dependence between the response output gain and the input signal frequency, the noise parameters of the system, etc., which indicates that the bona fide resonance and the generalized SR phenomena appear. Furthermore, the fluctuation noise, the number of particles, and the fractional order work together, producing more complex dynamic phenomena compared with the integral-order system. In addition, all the theoretical analyses are supported by the corresponding numerical simulations. We believe that the results that we have found may be a certain reference value for the research and development of the SR.

Collective behavior of globally coupled Langevin equations with colored noise in the presence of stochastic resonance.

The long-time collective behavior of globally coupled Langevin equations in a dichotomous fluctuating potential driven by a periodic source is investigated. By describing the collective behavior using the moments of the mean field and single-particle displacements, we study stochastic resonance and synchronization using the exact steady-state solutions and related stability criteria. Based on the simulation results and the criterion of the stationary regime, the notable differences between the stationary and nonstationary regimes are demonstrated. For the stationary regime, stochastic resonance with synchronization is discussed, and for the nonstationary regime, the volatility clustering phenomenon is observed.

Stochastic resonance phenomenon in Monte Carlo simulations of silver adsorbed on gold

The possibility of observing the stochastic resonance phenomenon was analyzed by means of Monte Carlo simulations of silver adsorbed on 100 gold surfaces. The coverage degree was studied as a function of the periodical variation of the chemical potential. The signal-noise relationship was studied as a function of the amplitude and frequency of chemical potential and temperature. When this value is plotted as a function of temperature, a maximum is found, indicating the possible presence of stochastic resonance.

Key role of coupling, delay, and noise in resting brain fluctuations

A growing body of neuroimaging research has documented that, in the absence of an explicit task, the brain shows temporally coherent activity. This so-called "resting state" activity or, more explicitly, the default-mode network, has been associated with daydreaming, free association, stream of consciousness, or inner rehearsal in humans, but similar patterns have also been found under anesthesia and in monkeys. Spatiotemporal activity patterns in the default-mode network are both complex and consistent, which raises the question whether they are the expression of an interesting cognitive architecture or the consequence of intrinsic network constraints. In numerical simulation, we studied the dynamics of a simplified cortical network using 38 noise-driven (Wilson-Cowan) oscillators, which in isolation remain just below their oscillatory threshold. Time delay coupling based on lengths and strengths of primate corticocortical pathways leads to the emergence of 2 sets of 40-Hz oscillators. The sets showed synchronization that was anticorrelated at <0.1 Hz across the sets in line with a wide range of recent experimental observations. Systematic variation of conduction velocity, coupling strength, and noise level indicate a high sensitivity of emerging synchrony as well as simulated blood flow blood oxygen level-dependent (BOLD) on the underlying parameter values. Optimal sensitivity was observed around conduction velocities of 1-2 m/s, with very weak coupling between oscillators. An additional finding was that the optimal noise level had a characteristic scale, indicating the presence of stochastic resonance, which allows the network dynamics to respond with high sensitivity to changes in diffuse feedback activity.

Stochastic resonance in auditory steady-state responses in a magnetoencephalogram

Objective To see whether stochastic resonance can be triggered in the auditory steady-state responses (ASSRs) in a magnetoencephalogram (MEG). Methods We measured ASSRs to 1 kHz sinusoidal tone modulated at 40 Hz with various intensities of white noise and obtained its power and degree of phase synchrony. Results Group statistics showed a significant enhancement in phase synchrony of ASSR by the presence of white noise of appropriate intensity. Tests on individual subjects showed that the data of four out of nine subjects exhibited enhancements in power or phase synchrony. Conclusions The ASSRs exhibit stochastic resonance of the so-called I-type (I for information) shown in phase synchrony when responding to modulated sinusoidal sound superimposed with weak white noise. Significance The gamma-band component and other oscillatory components in the brain activity have been recently ascribed by some researchers to the result of stochastic resonance caused by internal noise in the brain. Therefore the presence of stochastic resonance in ASSRs may be evidence to the hypothesis that ASSRs are related to the ongoing gamma-band component.

An exactly solvable linear model giving indication of stochastic resonance

The linear stochastic equation dx β /dt+[1+f β (t)]x β (t)=A sin (Ωt) is discussed. The functionƒ β (t) is defined as a Poissonian noise dependent on a parameterβ>0,ƒ β (t)=β Σ j [δ(t − t + ) −δ (t − t − )]. The mean frequency of the delta-pulses is chosen asβ-dependent in the formλ(β)=2γ(β −2 + 1) exp(−β) whereγ is a constant from the interval (0, 0.974). With the stochastic functionƒ β (t) defined in this way, attention is paid on the oscillational term of the averaged function 〈x(t)〉, 〈x(t)〉osc=Āsin(Ωt − α). It is found that the dependenceĀ=Ā(β) exhibits one maximum and one minimum. The occurrence of these extrema seems to affirm the presence of stochastic resonance.