Noise and coupling induced synchronization in a network of chaotic neurons

The synchronization in four forced FitzHugh–Nagumo (FHN) systems is studied, both experimentally and by numerical simulations of a model. We show that synchronization may be achieved either by coupling of systems through bidirectional diffusive interactions, by introducing a common noise to all systems or by combining both ingredients, noise and coupling together. Here we consider white and colored noises, showing that the colored noise is more efficient in synchronizing the systems respect to white noise. Moreover, a small addition of common noise allows the synchronization to occur at smaller values of the coupling strength. When the diffusive coupling in the absence of noise is considered, the system undergoes the transition to subthreshold oscillations, giving a spike suppression regime. We show that noise destroys the appearance of this dynamical regime induced by coupling.     

Representation of systems disturbed by wide band noise

In this paper, a method of handling and working with wide band noise is developed. We represent wide band noise as a distributed delay of white noise and use it to reduce a nonlinear system disturbed by wide band noise to a nonlinear system disturbed by white noise. An application of this reduction to a nonlinear filtering problem under a wide band noise disturbance is discussed.     

Numerical resolution of stochastic focusing NLS equations

In this note, we numerically investigate a stochastic nonlinear Schrödinger equation derived as a perturbation of the deterministic NLS equation. The classical NLS equation with focusing nonlinearity of power law type is perturbed by a random term; it is a strong perturbation since we consider a space-time white noise. It acts either as a forcing term (additive noise) or as a potential (multiplicative noise). For simulations made on a uniform grid, we see that all trajectories blow-up in finite time, no matter how the initial data are chosen. Such a grid cannot represent a noise with zero correlation lengths, so that in these experiments, the noise is, in fact, spatially smooth. On the contrary, we simulate a noise with arbitrarily small scales using local refinement and show that in the multiplicative case, blow-up is prevented by a space-time white noise. We also present results on noise induced soliton diffusion.     

Effect of bounded noise on chaotic motions of stochastically perturbed slowly varying oscillator

The effect of bounded noise on the chaotic behavior of a class of slowly varying oscillators is investigated. The stochastic Melnikov method is employed and then the criteria in both mean and mean-square sense are derived. The threshold amplitude of bounded noise given by stochastic Melnikov process is in good comparison with one determined by the numerical simulation of top Lyapunov exponents. The presence of noise scatters the chaotic domain in parameter space and the larger noise intensity results in a sparser and more irregular region. Both the simple cell mapping method and the generalized cell mapping method are applied to demonstrate the effects of noises on the attractors. Results show that the attractors are diffused and smeared by bounded noise and if the noise intensity increases, the diffusion is exacerbated.     

Effect of bounded noise on chaotic motion of duffing oscillator under parametric excitation

A harmonic function with constant amplitude and random frequency and phase is called bounded noise. In this paper, the effect of bounded noise on the chaotic behavior of the Duffing oscillator under parametric excitation is studied in detail. The random Melnikov process is derived and a mean-square criterion is used to detect the chaotic dynamics in the system. It is found that the threshold of bounded noise amplitude for the onset of chaos in the system increases as the intensity of the noise in frequency increases. The threshold of bounded noise amplitude for the onset of chaos is also determined by the numerical calculation of the largest Lyapunov exponents. The effect of bounded noise on the Poincaré map and power spectra is also investigated. The numerical results qualitatively confirm the conclusion drawn by using the random Melnikov process with mean-square criterion for larger noise intensity.     

Fuzzy based directional weighted median filter for impulse noise detection and reduction

The known median-based denoising methods tends to work well for restoring the images corrupted by random-valued impulse noise with low noise level, but it fails in denoising highly corrupted images. In this paper, a new noise reduction method based on directional weighted median based fuzzy impulse noise detection and reduction method (DWMFIDRM) has been proposed, which has been specially developed for denoising all categories of impulse noise. The contribution of this paper is threefold. The main contribution of the novel impulse noise reduction technique lies in the unification of three different methods; the impulse noise detection phase utilizing the concept of fuzzy gradient values, edge-preserving noise reduction phase based on the directional weighted median of the neighboring pixels and a final filtering step in order to deal with noisy pixels of non-zero degree. Such a unique combination has improved the efficiency of this method for high density noise removal. The experimental results of our proposed method have a significant improvement when compared to other existing filters for high density noise removal. This paper utilizes the concept of fuzzy gradient values. The noise reduction phase that preserves edge sharpness is based on the directional weighted median of neighboring pixels. Final filtering phase is performed only when there is non-zero degree of noise pixels. This phase makes our method more efficient in high noise density. Experimental results show that DWMFIDRM provides a significant improvement on other existing filters.     

Stochastic Evolution Equations Driven by a Fractional White Noise

Abstract

In this paper we study stochastic evolution equations driven by a fractional white noise with arbitrary Hurst parameter in infinite dimension. We establish the existence and uniqueness of a mild solution for a nonlinear equation with multiplicative noise under Lipschitz condition by using a fixed point argument in an appropriate inductive limit space. In the linear case with additive noise, a strong solution is obtained. Those results are applied to stochastic parabolic partial differential equations perturbed by a fractional white noise.     

Homogenization of a stochastically forced Hamilton-Jacobi equation

We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white in time. It is shown that the homogenized equation is deterministic, and, in general, the noise has an enhancement effect, for which we provide a quantitative estimate. As an application, we perform a noise sensitivity analysis for Hamilton-Jacobi equations forced by a noise term with small amplitude, and identify the scaling at which the macroscopic enhancement effect is felt. The results depend on new, probabilistic estimates for the large scale Hölder regularity of the solutions, which are of independent interest.     

基于敏感性的结构损伤识别中的噪声分析

针对基于振动测试的结构损伤识别方法很容易受到环境噪声干扰的问题,提出了一种新的噪声分析方法,并结合Monte Carlo 数值模拟技术研究了测量噪声对基于敏感性的损伤识别方法的影响．与普遍采用的摄动法不同,提出的方法直接由敏感性矩阵的Moore-Penrose广义逆推导得出．该方法不仅使得噪声分析过程更简洁而有效,并且能同时分析频率和振型噪声对于识别结果的影响．针对3种常用的基于敏感性的损伤识别方法,通过一个单层门式框架的仿真研究,表明了所提出的噪声分析方法的正确性和有效性．     

The effect of Gaussian white noise on the fractality of fluctuations in the plasma of a symmetrical discharge

In this work we investigate the influence of white Gaussian noise on the fluctuations in the plasma of a symmetrical discharge using multifractal detrended fluctuation analysis. We observe that in the range of noise intensity used in our study, the multifractality strength is increased by the noise, at all values of the inter-anode voltage, both for original and filtered time-series. This is interpreted as a new positive influence of noise because this effect can be understood as an increasing in the predictability on the dynamics in a time-series. A constructive influence of noise can appear only for fluctuations with underlying chaotic dynamics. The shuffling analysis demonstrates that the multifractality is purely a consequence of the correlations of the fluctuations. The noise influence is also observed in the change of the position of the maximum in the singularity spectra. The multifractal detrended cross correlation between light intensity and current intensity demonstrates that the fluctuations in both parameters are generated by the same physical processes though they are very different in nature: one is a local parameter and the other is a global one.     

Effect of noise on the pattern formation in an epidemic model

We present novel numerical evidence of complicated phenomenon controlled by noise in a spatial epidemic model. The number of the spot is decreased as the noise intensity being increased, which we show by performing a series of numerical simulations. Moreover, when the noise intensity and temporal correlation are both large enough, the model dynamics exhibits a noise controlled transition from spotted pattern to stripe growth. In addition to that, we show in details the number of the spotted and stripe pattern, with the identification of a wide range of noise intensity and temporal correlation. The obtained results show that noise plays an important role in the pattern formation of the epidemic model, which may provide guidance to prevent and control the spread of disease. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

“Chaos” in superregenerative receivers

The superregenerative principle has been known since the early 1920s. The circuit is extremely simple and extremely sensitive. Today, superheterodyne receivers generally supplant superregenerative receivers in most applications because there are several undesirable characteristics: poor selectivity, reradiation, etc. Superregenerative receivers undergo a revival in recent papers for wireless systems, where low cost and very low power consumption are relevant: house/building meters (such as water, energy, gas counter), personal computer environment (keyboard, mouse), etc. Another drawback is the noise level which is higher than that of a well-designed superheterodyne receiver; without an antenna input signal, the output of the receiver hears in an earphone as a waterfall noise; this sound principally is the inherent input noise amplified and detected by the circuit; however, when the input noise is negligible with respect of an antenna input signal, we are faced to an other source of “noise” self-generated by the superregenerative working. The main objective of this paper concerns this self-generated noise coming from an exponential growing followed by a re-injection process for which the final state is a function of the phase of the input signal.     

Using an adaptive neuro-fuzzy inference system-based interpolant for impulsive noise suppression from highly distorted images

A new impulsive noise (IN) suppression filter, entitled Adaptive neuro-fuzzy inference system (ANFIS)-based impulsive noise suppression Filter, which shows a high performance at the restoration of images distorted by IN, is proposed in this paper. The extensive simulation results show that the proposed filter achieves a superior performance to the other filters mentioned in this paper in the cases of being effective in noise suppression and detail preservation, especially when the noise density is very high.     

Noise-induced effects in nonlinear relaxation of condensed matter systems

Noise-induced phenomena characterise the nonlinear relaxation of nonequilibrium physical systems towards equilibrium states. Often, this relaxation process proceeds through metastable states and the noise can give rise to resonant phenomena with an enhancement of lifetime of these states or some coherent state of the condensed matter system considered. In this paper three noise induced phenomena, namely the noise enhanced stability, the stochastic resonant activation and the noise-induced coherence of electron spin, are reviewed in the nonlinear relaxation dynamics of three different systems of condensed matter: (i) a long-overlap Josephson junction (JJ) subject to thermal fluctuations and non-Gaussian, Lévy distributed, noise sources; (ii) a graphene-based Josephson junction subject to thermal fluctuations; (iii) electrons in a n-type GaAs crystal driven by a fluctuating electric field. In the first system, we focus on the switching events from the superconducting metastable state to the resistive state, by solving the perturbed stochastic sine-Gordon equation. Nonmonotonic behaviours of the mean switching time versus the noise intensity, frequency of the external driving, and length of the junction are obtained. Moreover, the influence of the noise induced solitons on the mean switching time behaviour is shown. In the second system, noise induced phenomena are observed, such as noise enhanced stability (NES) and stochastic resonant activation (SRA). In the third system, the spin polarised transport in GaAs is explored in two different scenarios, i.e. in the presence of Gaussian correlated fluctuations or symmetric dichotomous noise. Numerical results indicate an increase of the electron spin lifetime by rising the strength of the random fluctuating component. Furthermore, our findings for the electron spin depolarization time as a function of the noise correlation time point out (i) a non-monotonic behaviour with a maximum in the case of Gaussian correlated fluctuations, (ii) an increase up to a plateau in the case of dichotomous noise. The noise enhances the coherence of the spin relaxation process.     

Noise can create periodic behavior and stabilize nonlinear diffusions

It is shown that unlike nondegenerate (linear) diffusion processes, nonlinear diffusion processes can have a periodic law. We provide an example of a nonlinear diffusion for which periodic behavior is even created by the noise, i.e. no periodicity occurs when the noise is turned off. In the second part of the paper we give an example of a one-dimensional nonlinear diffusion which can be stabilized by noise. Finally we show also that the N-dimensional (N ≥ 2) ‘linear’ diffusion approximations of that system are stabilized by noise.     

Martingale Solution to Equations for Differential Type Fluids of Grade Two Driven by Random Force of Lévy Type

In this article we study a system of nonlinear non-parabolic stochastic evolution equations driven by Lévy noise type. This system describes the motion of second grade fluids driven by random force. Global existence of a martingale solution is proved under general conditions on the noise. Since the coefficient of the noise does not satisfy a Lipschitz property, we could not prove any pathwise uniqueness result. We note that this is the first work dealing with a stochastic model for non-Newtonian fluids excited by external forces of Lévy noise type.     

Log-Harnack inequality for mild solutions of SPDEs with multiplicative noise

Due to technical reasons, existing results concerning Harnack type inequalities for SPDEs with multiplicative noise apply only to the case where the coefficient in the noise term is a Hilbert–Schmidt perturbation of a constant bounded operator. In this paper we obtained gradient estimates, log-Harnack inequality for mild solutions of general SPDEs with multiplicative noise whose coefficient is even allowed to be unbounded which cannot be Hilbert–Schmidt. Applications to stochastic reaction–diffusion equations driven by space–time white noise are presented.     

Stability,coherent spiking and synchronization in noisy excitable systems with coupling and internal delays

We study the onset and the adjustment of different oscillatory modes in a system of excitable units subjected to two forms of noise and delays cast as external or internal according to whether they are associated with inter- or intra-unit activity. Conditions for stability of a single unit are derived in case of the linearized perturbed system, whereas the interplay of noise and internal delay in shaping the oscillatory motion is analyzed by the method of statistical linearization. It is demonstrated that the internal delay, as well as its coaction with external noise, drive the unit away from the bifurcation controlled by the excitability parameter. For the pair of interacting units, it is shown that the external/internal character of noise primarily influences frequency synchronization and the competition between the noise-induced and delay-driven oscillatory modes, while coherence of firing and phase synchronization substantially depend on internal delay. Some of the important effects include: (i) loss of frequency synchronization under external noise; (ii) existence of characteristic regimes of entrainment, where under variation of coupling delay, the optimized unit (noise intensity fixed at resonant value) may be controlled by the adjustable unit (variable noise) and vice versa, or both units may become adjusted to coupling delay; (iii) phase synchronization achieved both for noise-induced and delay-driven modes.     

External perturbation manifested system size resonance in a mesoscopic hormone signaling model

In mesoscopic reaction systems that contain only finite number of reactants, molecular fluctuation (or the so called internal noise), which can be characterized by the system size, plays an important role in nonlinear systems. In this work, the effect of internal noise is studied in a mesoscopic hormone signaling model with the presence of external perturbations (noise or signal). Simulation results reveal that the internal noise can play a constructive role to optimize the regularity of the noise induced internal signal only when external perturbation is present. This is a novel external perturbations induced system size resonance, which indicates that in complex mesoscopic systems, the system can automatically avoid the destructive environmental effects by tuning its size. Such kind of nontrivial cooperative effect may attribute to the fact that external perturbations broadened the regulation scope of the key mutual feedback. Therefore, current finding is of practical significance for similar physiological systems where the intercellular regulation plays the dominate role for signaling.     

Asymmetric non-Gaussian effects in a tumor growth model with immunization

The dynamical evolution of a tumor growth model, under immune surveillance and subject to asymmetric non-Gaussian α-stable Lévy noise, is explored. The lifetime of a tumor staying in the range between the tumor-free state and the stable tumor state, and the likelihood of noise-induced tumor extinction, are characterized by the mean residence time and the escape probability, respectively. For various initial densities of tumor cells, the mean residence time and the escape probability are computed with different noise parameters. It is observed that unlike the Gaussian noise or symmetric non-Gaussian noise, the asymmetric non-Gaussian noise plays a constructive role in the tumor evolution in this simple model. By adjusting the noise parameters, the mean residence time can be shortened and the escape probability can be increased, simultaneously. This suggests that a tumor may be mitigated with higher probability in a shorter time, under certain external environmental stimuli.