Stochastic resonance in a stochastic bistable system subject to additive white noise and dichotomous noise

The stochastic resonance (SR) in a stochastic stable system driven by a static force and a periodic square-wave signal as well as by additive white noise and dichotomous noise is considered from the point of view of the signal-to-noise ratio (SNR). It is found that the SNR exhibits SR behavior when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as well as when plotted as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise is investigated.     

Stochastic resonance in a bistable system with time-delayed feedback and non-Gaussian noise

The phenomenon of stochastic resonance in a bistable system with time-delayed feedback driven by non-Gaussian noise is investigated. Combining the small time delay approximation, the path-integral approach and the unified colored noise approximation, a general approximate Fokker–Planck equation of a stochastic system is obtained. The effects of the parameter q indicating the departure from the Gaussian noise, the delay time τ  , and the correlation time τ₀${\tau }_0$ of the non-Gaussian noise on the quasi-steady-state probability distribution function (SPD) and the signal-to-noise ratio (SNR) are discussed. It is found that the number of peaks in SPD and the reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR depends on the parameter q, the delay time τ  , and the noise correlation time τ₀${\tau }_0$.     

Stochastic resonance of a periodically driven neuron under non-Gaussian noise

We investigate the first-passage-time statistics of the integrate-fire neuron model driven by a sub-threshold harmonic signal superposed with a non-Gaussian noise. Here, we considered the noise as the result of a random multiplicative process displaced from the origin by an additive term. Such a mechanism generates a power-law distributed noise whose characteristic decay exponent can be finely tuned. We performed numerical simulations to analyze the influence of the noise non-Gaussian character on the stochastic resonance condition. We found that when the noise deviates from Gaussian statistics, the resonance condition occurs at weaker noise intensities, achieving a minimum at a finite value of the distribution function decay exponent. We discuss the possible relevance of this feature to the efficiency of the firing dynamics of biological neurons, as the present result indicates that neurons would require a lower noise level to detect a sub-threshold signal when its statistics departs from Gaussian.     

Stochastic resonance and heat fluctuations in a driven double-well system

We study a periodically driven (symmetric as well as asymmetric) double-well potential system at finite temperature. We show that mean heat loss by the system to the environment (bath) per period of the applied field is a good quantifier of stochastic resonance. It is found that the heat fluctuations over a single period are always larger than the work fluctuations. The observed distributions of work and heat exhibit pronounced asymmetry near resonance. The heat loss over a large number of periods satisfies the conventional steady-state fluctuation theorem.     

Correlated noise induced spatiotemporal coherence resonance in a square lattice network

The effects of additive correlated noise, which is composed of common Gaussian white noise and local Gaussian colored noise, on a square lattice network locally modelled by the Rulkov map are studied. We focus on the ability of noise to induce pattern formation in a resonant manner. It is shown that local Gaussian colored noise is able to induce pattern formation, which is more coherent at some noise intensity or correlation time, so it is able to induce spatiotemporal coherence resonance in the network. When common Gaussian white noise is applied in addition, it is seen that the correlated noise can induce coherent spatial structures at some intermediate noise correlation, while this is not the case for smaller and larger noise intensities. The mechanism of the observed spatiotemporal coherence resonance is discussed. It is also found that the correlation time of local colored noise has no evident effect on the optimal value of the noise strength for spatiotemporal coherence resonance in the network.     

Stochastic resonance in FitzHugh-Nagumo system with time-delayed feedback

The dynamics of a periodically driven FitzHugh-Nagumo system with time-delayed feedback and Gaussian white noise is investigated. The stochastic resonance which is characterized by the Fourier coefficient Q is numerically calculated. It is found that the stochastic resonance of the system is a non-monotonic function of the noise strength and the signal period. The variation of the time-delayed feedback can induce periodic stochastic resonance in the system.     

Stochastic resonance in time-delayed bistable systems driven by weak periodic signal

We study theoretically a bistable system with time-delayed feedback driven by a weak periodic force. The effective potential function and the steady-state probability density are derived. The delay time and the strength of its feedback can change the shapes of the potential wells. In the adiabatic approximation, the signal-to-noise ratio (SNR) of the system with a weak periodic force is obtained. The time-delayed feedback modulates the magnitude of SNR by changing the shape of the potential and the effective strength of the signal. The maximum of SNR decreases with increasing the feedback intensity ?. When ? is negative (or positive), the time delay can suppress (or promote) the stochastic resonance phenomenon.     

Mean First-Passage Time in a Bistable Kinetic Model with Stochastic Potentials

The transient properties of a bistable system with the stochastic potentials are investigated. The explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The results show that the MFPT of the system increases with the amplitude Δ of the stochastic potential, decreases with the noise intensity D and the correlation length l. The stochastic potential makes against the particle moving towards the destination.     

Entropic Stochastic Resonance Driven by Colored Noise

The phenomenon of entropic stochastic resonance （ESR） in a two-dimensional confined system driven by a transverse periodic force is investigated when the colored fluctuation is included in the system. Applying the method of unified colored noise approximation, the approximate Fokker-Planck equation can be derived in the absence of the periodic force. Through the escaping rate of the Brownian particle from one well to the other, the power spectral amplification can be obtained. It is found that increasing the values of the noise correlation time and the signal frequency can suppress the ESR of the system.     

Stochastic resonance: influence of a f-κ noise spectrum

With the aim of studying stochastic resonance (SR) in a double-well potential when the noise source has a spectral density of the form f^-κ (with varying κ), we have extended a procedure introduced by Kaulakys et al. (Phys. Rev. E 70, 020101 (2004)). In order to achieve an analytical understanding of the results, we have obtained an effective Markovian approximation that allows us to make a systematic study of the effect of such noise on the SR phenomenon. A comparison of the numerical and analytical results shows an excellent qualitative agreement indicating that the effective Markovian approximation is able to correctly describe the general trends.     

Stochastic Simulation of Turing Patterns

We investigate the effects of intrinsic noise on Turing pattern formation near the onset of bifurcation from the homogeneous state to Turing pattern in the reaction-diffusion Brusselator. By performing stochastic simulations of the master equation and using Gillespie＇s algorithm, we check the spatiotemporal behaviour influenced by internal noises. We demonstrate that the patterns of occurrence frequency for the reaction and diffusion pro- cesses are also spatially ordered and temporally stable. Turing patterns are found to be robust against intrinsic fluctuations. Sfochastic simulations also reveal that under the influence of intrinsic noises, the onset of Turing instability is advanced in comparison to that predicted deterministically.     

Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System

We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.     

A Coarse Estimation of Cell Size Region from a Mesoscopic Stochastic Cell Cycle Model

Based on a deterministic cell cycle model of fission yeast, the effects of the finite cell size on the cell cycle regulation in wee1- cdc25△ double mutant type are numerically studied by using of the chemical Langevin equations. It is found that at a certain region of cell size, our numerical results from the chemical Langevin equations are in good qualitative agreement with the experimental observations. The two resettings to the G2 phase from early stages of mitosis can be induced under the moderate cell size. The quantized cycle times can be observed during such a cell size region. Therefore, a coarse estimation of cell size is obtained from the mesoscopic stochastic cell cycle model.     

Control coherence resonance by noise recycling

We study the effect of recycled noise, generated by the superposition of a primary Gaussian noise source with a second component of constant delay, in a parameter region below the threshold of supercritical Hopf bifurcation, by focussing on the performance of noise induced oscillations and coherence resonance. For fixed noise intensity, the amplitude and signal-to-noise ratio of the oscillation show periodic dependences on the delay time. The optimal noise intensity for the occurrence of coherence resonance also shows a periodic dependence on the delay. A theoretical analysis based on the stochastic normal form theory is presented, which qualitatively reproduces the simulation results with good agreement. This work presents a possible strategy for controlling noise induced oscillations and coherence resonance by deliberately adjusting the parameters of the recycled noise.     

Stochastic synchronization of coupled neural networks with intermittent control

In this Letter, we study the exponential stochastic synchronization problem for coupled neural networks with stochastic noise perturbations. Based on Lyapunov stability theory, inequality techniques, the properties of Weiner process, and adding different intermittent controllers, several sufficient conditions are obtained to ensure exponential stochastic synchronization of coupled neural networks with or without coupling delays under stochastic perturbations. These stochastic synchronization criteria are expressed in terms of several lower-dimensional linear matrix inequalities (LMIs) and can be easily verified. Moreover, the results of this Letter are applicable to both directed and undirected weighted networks. A numerical example and its simulations are offered to show the effectiveness of our new results.     

Stochastic Resonance in the Tumour Cell Growth Model

The phenomenon of stochastic resonance （SR） in the tumour cell growth model subjected cross-correlated noises is investigated. When a weakly periodic signal is added to the system, the signal-to-noise ratio RSNR is derived by the quasi-steady-state probability distribution function and the adiabatic elimination method. Based on the derived RSNR, the effects of these parameters （the cross-correlated strength λ and the cross-correlated time τ） are analysed by numerical calculation. It is found that the existence of a maximum in RSNR is the identifying characteristic of the SR phenomenon. The maximum of RsNR decreases with the increase of λ and increases with the increase of τ.     

Stochastic resonance on Newman-Watts networks of Hodgkin-Huxley neurons with local periodic driving

We study the phenomenon of stochastic resonance on Newman-Watts small-world networks consisting of biophysically realistic Hodgkin-Huxley neurons with a tunable intensity of intrinsic noise via voltage-gated ion channels embedded in neuronal membranes. Importantly thereby, the subthreshold periodic driving is introduced to a single neuron of the network, thus acting as a pacemaker trying to impose its rhythm on the whole ensemble. We show that there exists an optimal intensity of intrinsic ion channel noise by which the outreach of the pacemaker extends optimally across the whole network. This stochastic resonance phenomenon can be further amplified via fine-tuning of the small-world network structure, and depends significantly also on the coupling strength among neurons and the driving frequency of the pacemaker. In particular, we demonstrate that the noise-induced transmission of weak localized rhythmic activity peaks when the pacemaker frequency matches the intrinsic frequency of subthreshold oscillations. The implications of our findings for weak signal detection and information propagation across neural networks are discussed.     

Phase separation in binary systems with internal multiplicative noise

A study of a phase separation process in stochastic systems with a field dependent kinetic coefficient and an internal multiplicative noise is presented. Dynamics of spinodal decomposition at early and late stages is investigated by computer simulations where the domain growth law is generalized. A mean field approach was carried out in order to obtain the stationary probability, bifurcation and phase diagrams displaying reentrant phase transitions. We relate our approach to entropy driven phase transitions theory.     

Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the stationary limit. If magnetic field is smaller compared to the critical value, determined by frictional anisotropy, the relaxation of the correlation is non-oscillating in time. However, in a larger magnetic field this relaxation becomes oscillating. The phenomenon is related to the statistical dependence of the components of transformed random force caused by the simultaneous influence of magnetic field and anisotropic dissipation.