Noise Correlation Time Research Articles

Inverse stochastic resonance induced by non-Gaussian colored noise

Abstract This paper mainly studies the phenomenon of inverse stochastic resonance induced by non-Gaussian noise in a representative Hodgkin–Huxley model. Firstly, spiking manners of neurons under different input currents are investigated and different current thresholds and bifurcation diagram are given. Besides, the limit cycle with different input current are plotted. Then, taking the average firing rate as a measurement, the result shows that a minimum exists in the curve corresponding to the intensity, correlation time and deviation coefficient of non-Gaussian noise, which is named inverse stochastic resonance(ISR). More important, it is found that the mean firing rate will remain unchanged with noise intensity and deviation coefficient when correlation time is sufficiently large and finally trends toward a constant value which is completely determined by input current. Further, the present results will be benefit to investigate the functional roles of randomness in neural spiking.

Stochastic Differential Equation Model for Spontaneous Emission and Carrier Noise in Semiconductor Lasers

We present a new stochastic differential equation model for the spontaneous emission noise and carrier noise in semiconductor lasers. The correlations between these two types of noise have often been neglected in recent studies of the effects of the noise on the laser dynamics. However, the classic results of Henry show that the intensity noise and the carrier noise are strongly negatively correlated. Our model demonstrates how to properly account for these correlations since the corresponding diffusion coefficients agree exactly with those derived by Henry. We show that in fact in the correct model the spontaneous emission noise and the carrier noise are driven by the same Wiener processes. Furthermore, we demonstrate that the nonzero correlation time of the physical noise affects the mean dynamics of both the electric field amplitude and the carrier number. We show that these are systematic corrections that can be described by additional drift terms in the model.

Colored Gaussian noises induced stochastic resonance and stability transition for an insect growth system driven by a multiplicative periodic signal

In this paper, we focus on investigating the steady-state shift behaviors and the stochastic resonance phenomenon (SR) for a biological insect population system with a multiplicative periodic signal caused by the terms of the colored multiplicative and additive noises. Our research results imply that the multiplicative noise and the self-correlation of the additive noise can weaken the stability of the biological system and restrain the growth of the insect population, while the additive noise and the self-correlation time of the multiplicative noise can strengthen the stability of the insect system and facilitate the biological population to breed. As regards to the phenomenon of the SR evoked by a multiplicative periodic signal, noise terms and their correlation times, the computed results show that the additive noise intensity M and the self- correlation time τ1 of the multiplicative noise can both improve the SR effect. Inversely, the multiplicative noise intensity Q and the self-correlation time τ2 of the additive noise can suppress together the SR phenomenon. Whereas, it should be pointed out that in the SNR-Q and SNR-M plots, the two self-correlation times can both motivate a resonant peak, but not change the peak value of the SNR no matter how the two noise correlation times vary.

Statistical Characteristics of the Gaussian-Noise Spikes Exceeding the Specified Threshold as Applied to Discharges in a Thundercloud

We obtain expressions for the probabilities of the normal-noise spikes with the Gaussian correlation function and for the probability density of the inter-spike intervals. As distinct from the delta-correlated noise, in which the intervals are distributed by the exponential law, the probability of the subsequent spike depends on the previous spike and the interval-distribution law deviates from the exponential one for a finite noise-correlation time (frequency-bandwidth restriction). This deviation is the most pronounced for a low detection threshold. Similarity of the behaviors of the distributions of the inter-discharge intervals in a thundercloud and the noise spikes for the varying repetition rate of the discharges/spikes, which is determined by the ratio of the detection threshold to the root-mean-square value of noise, is observed. The results of this work can be useful for the quantitative description of the statistical characteristics of the noise spikes and studying the role of fluctuations for the discharge emergence in a thundercloud.

Diffusion of Brownian particles in a tilted periodic potential under the influence of an external Ornstein–Uhlenbeck noise

The diffusion behaviors of Brownian particles in a tilted periodic potential under the influence of an internal white noise and an external Ornstein–Uhlenbeck noise are investigated through numerical simulation. In contrast to the case when the bias force is smaller or absent, the diffusion coefficient exhibits a nonmonotonic dependence on the correlation time of the external noise when bias force is large. A mechanism different from locked-to-running transition theory is presented for the diffusion enhancement by a bias force in intermediate to large damping. In the underdamped regime and the presence of external noise, the diffusion coefficient is a monotonically decreasing function of low temperature rather than a nonmonotonic function when external noise is absent. The diffusive process undergoes four regimes when bias force approaches but is less than its critical value and noises intensities are small. These behaviors can be attributed to the locked-to-running transition of particles.

Coherence resonance induced by cross-correlated sine-Wiener noises in the FitzHugh–Nagumo neurons

We study coherence resonance (CR) in the FitzHugh–Nagumo (FHN) neurons under cross-correlated sine-Wiener (CCSW) noises. It is numerically demonstrated that the reciprocal coefficient of variance of inter-spike intervals (R) increases with increasing amplitude or correlation time of CCSW noises, reaches the maximum at proper amplitude or correlation time, and then decreases, suggesting the appearance of CR phenomenon. In addition, the occurrence of CR is sensitive to a parameter range of amplitudes and correlation times of CCSW noises. Thus, CR can be controlled by regulating the amplitudes and correlation times of CCSW noises in the FHN excitable systems.

Transport phenomena in intracellular calcium dynamics driven by non-Gaussian noises

The role of non-Gaussian noises on transport characteristic of Ca2+ in intracellular calcium oscillation system driven by non-Gaussian noises is studied by means of second-order stochastic Runge–Kutta type algorithm. The statistical properties of velocity of cytosolic and calcium store’s Ca2+ concentration are simulated. The results exhibit, as parameter p(which is used to control the degree of the departure from the non-Gaussian noise and Gaussian noise.)increases, calcium in cytosol shows positive, zero, and negative transport, but in calcium store always hold positive value. As non-Gaussian noises increase, calcium in cytosol appears negative and zero transport, and in calcium store appears positive transport. As correlation time of non-Gaussian noises varies, calcium in both cytosol and calcium store occur negative, zero, and positive transport.

Nonlinear frequency transduction of nanomechanical Brownian motion

We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into frequency noise. This mechanism, ubiquitous to all weakly-nonlinear resonators thermalized to a bath, results in a phase diffusion process altering the motion: two limit behaviors appear, analogous to motional narrowing and inhomogeneous broadening in NMR. Their crossover is found to depend non-trivially on the ratio of the frequency noise correlation time to its magnitude. Our measurements obtained over an unprecedented range covering the two limits match the theory of Y. Zhang and M. I. Dykman, Phys. Rev. B 92, 165419 (2015), with no free parameters. We finally discuss the fundamental bound on frequency resolution set by this mechanism, which is not marginal for bottom-up nanostructures.

Computationally efficient joint imperceptible image watermarking and JPEG compression: a green computing approach

This paper presents a computationally efficient joint imperceptible image watermarking and joint photographic experts group (JPEG) compression scheme. In recent times, the transmission and storage of digital documents/information over the unsecured channel are enormous concerns and nearly all of the digital documents are compressed before they are stored or transmitted to save the bandwidth requirements. There are many similar computational operations performed during watermarking and compression which lead to computational redundancy and time delay. This demands development of joint watermarking and compression scheme for various multimedia contents. In this paper, we propose a technique for image watermarking during JPEG compression to address the optimal trade-off between major performance parameters including embedding and compression rates, robustness and embedding alterations against different known signal processing attacks. The performance of the proposed technique is extensively evaluated in the form of peak signal to noise ratio (PSNR), correlation, compression ratio and execution time for different discrete cosine transform (DCT) blocks and watermark sizes. Embedding is done on DCT coefficients using additive watermarking.

Numerical investigation of noise-enhanced stability phenomenon induced by bounded noise in a single stable system

The effects of bounded noise on the stability of the single stable system are investigated by the simulation method. The results indicate that: (1) The bounded additive noise can induce the noise-enhanced stability (NES) phenomenon and the correlation intensity between bounded additive and bounded multiplicative noises λ and noise correlation time τ can enhance the NES effect for the case of the bounded additive noise induced transition; (2) The bounded multiplicative noise can also induce the NES phenomenon only for larger value of the τ, however, the λ weaken the NES effect and the τ can also enhance the NES effect for the case of the multiplicative noise induced transition.

Regime shifts driven by dynamic correlations in gene expression noise.

Gene expression is a noisy process that leads to regime shifts between alternative steady states among individual living cells, inducing phenotypic variability. The effects of white noise on the regime shift in bistable systems have been well characterized, however little is known about such effects of colored noise (noise with nonzero correlation time). Here, we show that noise correlation time, by considering a genetic circuit of autoactivation, can have a significant effect on the regime shift between distinct phenotypic states in gene expression. We demonstrate this theoretically, using stochastic potential, stationary probability density function, and first-passage time based on the Fokker-Planck description, where the Ornstein-Uhlenbeck process is used to model colored noise. We find that an increase in noise correlation time in the degradation rate can induce a regime shift from a low to a high protein concentration state and enhance the bistable regime, while an increase in noise correlation time in the basal rate retains the bimodal distribution. We then show how cross-correlated colored noises in basal and degradation rates can induce regime shifts from a low to a high protein concentration state, but reduce the bistable regime. We also validate these results through direct numerical simulations of the stochastic differential equation. In gene expression understanding the causes of regime shift to a harmful phenotype could improve early therapeutic intervention in complex human diseases.

Probabilistic distribution and stochastic P-bifurcation of a hybrid energy harvester under colored noise

In this manuscript, a hybrid energy harvesting system combining piezoelectric and electromagnetic transduction and subjected to colored noise is investigated. By using the stochastic averaging method, the stationary probability density functions of amplitudes are obtained and reveal interesting dynamics related to the long term behavior of the device. From stationary probability densities, we discuss the stochastic bifurcation through the qualitative change which shows that noise intensity, correlation time and other system parameters can be treated as bifurcation parameters. Numerical simulations are made for a comparison with analytical findings. The Mean first passage time (MFPT) is numerical provided in the purpose to investigate the system stability. By computing the Mean residence time (TMR), we explore the stochastic resonance phenomenon; we show how it is related to the correlation time of colored noise and high output power.

Stochastic bifurcations of generalized Duffing–van der Pol system with fractional derivative under colored noise**Project supported by the National Natural Science Foundation of China (Grant No. 11302157), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2015JM1028), the Fundamental Research Funds for the Central Universities, China (Grant No. JB160706), and Chinese–Serbian Science and Technology Cooperation for the

The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation.

Nonequilibrium dynamics of a pure dry friction model subjected to colored noise.

We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose, we consider the motion of a particle subjected to dry friction and colored noise. The finite correlation time of the noise provides an additional dimension in phase space, causes a nontrivial probability current, and establishes a proper nonequilibrium regime. Furthermore, the setup allows for the study of stick-slip phenomena, which show up as a singular component in the stationary probability density. Analytic insight can be provided by application of the unified colored noise approximation, developed by Jung and Hänggi [Phys. Rev. A 35, 4464(R) (1987)0556-279110.1103/PhysRevA.35.4464]. The analysis of probability currents and of power spectral densities underpins the observed stick-slip transition, which is related with a critical value of the noise correlation time.

Stochastic resonance for a forest growth system subjected to non-Gaussian noises and a multiplicative periodic signal

In this paper, the stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a forest growth system which is excited by additive Gaussian noise, multiplicative non-Gaussian noise and noise correlation time is investigated. According to the fast descent method, the unified colored noise approximation and the SR theory, the analytical expression of the signal-to-noise ratio (SNR)is derived in the adiabatic limit. Via numerical calculations, each effect of the addictive noise intensity, the multiplicative noise intensity and the departure parameter from the Gaussian noise upon the signal-to-noise ratio (SNR) is discussed. It is shown that the addictive noise intensity always plays a significant role in stimulating the SR phenomenon. Conversely, the multiplicative noise intensity generally plays a remarkable role in restraining the effect of SR in most cases except for the case of M=0.01. Moreover, the noise correlation time can also excite the SR effect. On the other hand, the departure parameter from the Gaussian noise and the forest growth rate can produce entirely different effects on the SNR under the different conditions of the system parameters.

Array-enhanced logical stochastic resonance subject to colored noise

This paper proposes an approach that uses a parallel array to improve the reliability and robustness of logical stochastic resonance subject to colored noise. The experimental results demonstrate that (i) the increase of array size can extend the optimal range of noise intensity and increase the maximum probability of obtaining correct logic operation. (ii) The optimal range of noise correlation time is broadened with the increase of array size. (iii) The main difference between logical stochastic resonance subject to white noise and colored noise is that the increase of noise correlation time broadens the optimal range of noise intensity when the stochastic noise is colored noise. At the same time, the maximum probability of obtaining correct logic operation is close to 1. Therefore, reliable and robust logic gate can be realized under a certain array size.

Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems

Nonlinear relaxation phenomena in three different systems of condensed matter are investigated. (i) First, the phase dynamics in Josephson junctions is analyzed. Specifically, a superconductor-graphene-superconductor (SGS) system exhibits quantum metastable states, and the average escape time from these metastable states in the presence of Gaussian and correlated fluctuations is calculated, accounting for variations in the the noise source intensity and the bias frequency. Moreover, the transient dynamics of a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian noise sources is investigated. Noise induced phenomena are observed, such as the noise enhanced stability and the stochastic resonant activation. (ii) Second, the electron spin relaxation process in a n-type GaAs bulk driven by a fluctuating electric field is investigated. In particular, by using a Monte Carlo approach, we study the influence of a random telegraph noise on the spin polarized transport. Our findings show the possibility to raise the spin relaxation length by increasing the amplitude of the external fluctuations. Moreover, we find that, crucially, depending on the value of the external field strength, the electron spin depolarization length versus the noise correlation time increases up to a plateau. (iii) Finally, the stabilization of quantum metastable states by dissipation is presented. Normally, quantum fluctuations enhance the escape from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system, consisting of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath. We find that the escape time from the metastable region has a nonmonotonic behavior versus the system- bath coupling and the temperature, producing a stabilizing effect.

Multiplicative non-Gaussian noise and additive Gaussian white noise induced transition in a piecewise nonlinear model

We study the transition problems in a piecewise nonlinear model induced by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Firstly, applying the path integral approach, the unified colored noise approximation, the analytical expression of the steady-state probability density function (SPD) is derived. Then the change regulation of the SPD is analyzed with the change of the strength and relevance of multiplicative noise and additive noise. From numerical computations we obtain some new nonlinear phenomena: the transition can be induced by the cross-correlation strength between noises, the non-Gaussian noise intensity and the Gaussian noise intensity as well as the non-Gaussian noise deviation parameter. This indicates that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. Moreover, we also find the correlation time of the non-Gaussian noise can not induce the transition.

Non-Gaussian noises induce transitions in intracellular calcium dynamics

The effect of non-Gaussian noises on time series and stability of intracellular calcium oscillation is researched by means of second-order stochastic Runge–Kutta type algorithm. By simulating time series and stationary probability distribution of Ca2+ concentration in cytosol and calcium store, the results show: (i) the bigger parameter p(which is used to control the degree of the departure from the non-Gaussian noise and Gaussian noise.) would induce anti-synchronous quasi-periodic oscillation; (ii) the stability weakens as p increases, but strengthens as correlation time of non-Gaussian noises prolongs; (iii) the strong non-Gaussian noises induce transitions.

Response to a periodic stimulus in a perfect integrate-and-fire neuron model driven by colored noise.

The output interspike interval statistics of a stochastic perfect integrate-and-fire neuron model driven by an additive exogenous periodic stimulus is considered. The effect of temporally correlated random activity of synaptic inputs is modeled by an additive symmetric dichotomous noise. Using a first-passage-time formulation, exact expressions for the output interspike interval density and for the serial correlation coefficient are derived in the nonsteady regime, and their dependence on input parameters (e.g., the noise correlation time and amplitude as well as the frequency of an input current) is analyzed. It is shown that an interplay of a periodic forcing and colored noise can cause a variety of nonequilibrium cooperation effects, such as sign reversals of the interspike interval correlations versus noise-switching rate as well as versus the frequency of periodic forcing, a power-law-like decay of oscillations of the serial correlation coefficients in the long-lag limit, amplification of the output signal modulation in the instantaneous firing rate of the neural response, etc. The features of spike statistics in the limits of slow and fast noises are also discussed.