Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.

Effects of colored noise on the dynamics of quantum entanglement of a one-parameter qubit-qutrit system

We analyzed the effect of colored noise on the negativity dynamics of a hybrid system consisting of a qubit-qutrit and not interacting,prepared from the start in an entangled one-parameter state and acting with noise in local and non-local environments.In this pink and brown noise we investigated two different situations:in the first situation,the noise is produced by a bistable oscillator with an unknown exchange rate;however,in the second situation,the noise is generated by a set of bistable oscillators.We found that entanglement decreases with time to zero,and undergoes the phenomenon of sudden death and rebirth.The pink noise is more prone to entanglement than the brown noise and the non-local environment is more prone to entanglement than the local one.When the number of fluctuators is increased,entanglement decays faster and finally,for certain parameters of the initial state,the subsystems are not affected by the noise.

Nano-friction phenomenon of Frenkel-Kontorova model under Gaussian colored noise

The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova(FK)model under Gaussian colored noise is investigated by using the molecular dynamic simulation method.The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method.Via the stochastic Runge-Kutta algorithm,the relationship between different parameter values of the Gaussian colored noise(the noise intensity and the correlation time)and the nano-friction phenomena such as hysteresis,the maximum static friction force is separately studied here.Similar results are obtained from the two geometrically opposed ideal cases:incommensurate and commensurate interfaces.It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force,the introduction of noise can accelerate the motion of the system,making the atoms escape from the substrate potential well more easily.Interestingly,suitable correlation time and noise intensity give rise to super-lubricity.It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the incommensurate interface.

Operational modal parameter identification with colored noise excitation

Operational Modal Analysis(OMA) refers to the modal analysis of a structure in its operating state. The advantage of OMA is that only the output vibration signal of a system is used in the analysis process. Classic OMA is based on the white noise excitation assumption and many identification methods have been developed in both time domain and frequency domain. But in reality, many environmental excitations are not compliance with the white noise assumption. In this paper, a method of half power bandwidth analysis is applied to power spectrum analysis to deal with the colored noise and trapezoidal spectral excitation. The modal frequencies and modal damping ratios are derived and the error caused by trapezoidal spectral and colored noise excitation are analyzed. It is proved that the OMA algorithm based on the white noise assumption can be extended to the colored noise environments under certain conditions. Finally, a simulation example with a cantilever beam and a vibration test with four kinds of colored noise and trapezoidal spectrum base excitation are carried out and the results support the proposed method.

Influence of the Gaussian colored noise and electromagnetic radiation on the propagation of subthreshold signals in feedforward neural networks

Iterative methods are used to simulate the in vitro feedforward neural networks in physiological experiments.Emissivity can be propagated to a minimum of ten groups.However,the discharge activity of each group will be more synchronized.The feedforward neural networks have a wide range of applications in machine learning,and the weight of synapses considerably influences the propagation of weak signals.Herein,we investigated the effect of Gaussian colored noise and electromagnetic radiation on the propagation of the subthreshold excitatory postsynaptic current signals in the input layer of the multilayer Izhikevich neural feedforward networks.In the absence of electromagnetic radiation,the excitatory postsynaptic current signal is stably propagated and amplified in multilayer feedforward neural networks under the optimal Gaussian colored noise strength or correlation time in the output layer of the network.Compared with the case in which there is no electromagnetic radiation,the presence of electromagnetic radiation slightly reduces the propagation of weak signals.Further,the time required to propagate the excitatory postsynaptic current signal to the output layer increases with the increasing feedback gain.The feedforward neural network considered in this study is a considerably simple model.More complex structures,such as backward connection and delayed feedback,can be observed in real biological systems.Hence,the next step will be to study more complex neural models with neuron models based on the physiological experimental data and compare them with real biological systems.Furthermore,the study of neural networks can be combined with an experimental study about the auditory nervous system of bats to understand the biological mechanism associated with the auditory system function of bats from two perspectives.

Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs.When the parameter varies within a certain time scale,the rate will affect the tipping behaviors.These behaviors are undesirable in thermoacoustic systems,which are widely used in aviation,power generation and other industries.Thus,this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises.Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method.Then,the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions.Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption,which is called as a rate-dependent tipping-delay phenomenon.Besides,the influences of the initial values,the rate,the changing time of the parameters,and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail.These results are of great significance for research in related fields such as aviation and land gas turbines.

Posterior Cramér-Rao Bounds for Nonlinear Dynamic System with Colored Noises

A mean squared error lower bound for the discrete-time nonlinear filtering with colored noises is derived based on the posterior version of the Cramer-Rao inequality.The colored noises are characterized by the auto-regressive model including the auto-correlated process noise and autocorrelated measurement noise simultaneously.Moreover,the proposed lower bound is also suitable for a general model of nonlinear high order auto-regressive systems.Finally,the lower bound is evaluated by a typical example in target tracking.It shows that the new lower bound can assess the achievable performance of suboptimal filtering techniques,and the colored noise has a significantly effect on the lower bound and the performance of filters.

Noise color influence on escape times in nonlinear oscillators-experimental and numerical results

The interplay between noise and nonlinearites can lead to escape dynamics.Associated nonlinear phe-nomena have been observed in various applications ranging from climatology to biology and engineering.For reasons of computational ease,in most studies,Gaussian white noise is used.However,this noise model is not physical due to the associated infinite energy content.Here,the authors present extensive experimental investigations and numerical simulations conducted to examine the impact of noise color on escape times in nonlinear oscillators.With a careful parameterization of the numerical simulations,the authors are able to make quantitative comparisons with experimental results.Through the experi-ments and simulations,it is illustrated that the noise color can drastically influence escape times and escape probability.

Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises

The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits.To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation(FPE),we deal with the non-Gaussian colored noise and then adopt the unified colored noise approximation(UCNA).Subsequently,the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function(SPDF).The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect,which is in contrast to that of the uncorrelated Gaussian white noise case,where the parameter is absent from the governing equation,i.e.,the most probable steady states are mainly controlled by the uncorrelated multiplicative noise.Additionally,in comparison with the deterministic counterpart,some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise,the noise intensity,and the non-Gaussian noise deviation parameter are discussed.Moreover,the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned.Furthermore,the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo(MC)simulations of the original system.

Multi-Source Underwater DOA Estimation Using PSO-BP Neural Network Based on High-Order Cumulant Optimization

Due to the complex and changeable environment under water,the performance of traditional DOA estimation algorithms based on mathematical model,such as MUSIC,ESPRIT,etc.,degrades greatly or even some mistakes can be made because of the mismatch between algorithm model and actual environment model.In addition,the neural network has the ability of generalization and mapping,it can consider the noise,transmission channel inconsistency and other factors of the objective environment.Therefore,this paper utilizes Back Propagation(BP)neural network as the basic framework of underwater DOA estimation.Furthermore,in order to improve the performance of DOA estimation of BP neural network,the following three improvements are proposed.(1)Aiming at the problem that the weight and threshold of traditional BP neural network converge slowly and easily fall into the local optimal value in the iterative process,PSO-BP-NN based on optimized particle swarm optimization(PSO)algorithm is proposed.(2)The Higher-order cumulant of the received signal is utilized to establish the training model.(3)A BP neural network training method for arbitrary number of sources is proposed.Finally,the effectiveness of the proposed algorithm is proved by comparing with the state-of-the-art algorithms and MUSIC algorithm.

Tensor-Based Source Localization Method with EVS Array

In many wireless scenarios,e.g.,wireless communications,radars,remote sensing,direc-tion-of-arrival(DOA)is of great significance.In this paper,by making use of electromagnetic vec-tor sensors(EVS)array,we settle the issue of two-dimensional(2D)DOA,and propose a covari-ance tensor-based estimator.First of all,a fourth-order covariance tensor is used to formulate the array covariance measurement.Then an enhanced signal subspace is obtained by utilizing the high-er-order singular value decomposition(HOSVD).Afterwards,by exploiting the rotation invariant property of the uniform array,we can acquire the elevation angles.Subsequently,we can take ad-vantage of vector cross-product technique to estimate the azimuth angles.Finally,the polarization parameters estimation can be easily completed via least squares,which may make contributions to identifying polarization state of the weak signal.Our tensor covariance algorithm can be adapted to spatially colored noise scenes,suggesting that it is more flexible than the most advanced algorithms.Numerical experiments can prove the superiority and effectiveness of the proposed approach.

The Harmonic Oscillator with Random Damping in Non-Markovian Thermal Bath

In this paper, we define the harmonic oscillator with random damping in non-Markovian thermal bath. This model represents new version of the random oscillators. In this side, we derive the overdamped harmonic oscillator with multiplicative colored noise and translate it into the additive colored noise by changing the variables. The overdamped harmonic oscillator is stochastic differential equation driving by colored noise. We derive the change in the total entropy production (CTEP) of the model and calculate the mean and variance. We show the fluctuation theorem (FT) which is invalid at any order in the time correlation. The problem of the deriving of the CTEP is studied in two different examples of the harmonic potential. Finally, we give the conclusion and plan for future works.

Distributed Kalman filter for UWB/INS integrated pedestrian localization under colored measurement noise

Colored Measurement Noise(CMN)has a great impact on the accuracy of human localization in indoor environments with Inertial Navigation System(INS)integrated with Ultra Wide Band(UWB).To mitigate its influence,a distributed Kalman Filter(dKF)is developed for Gauss-Markov CMN with switching Colouredness Factor Matrix(CFM).In the proposed scheme,a data fusion filter employs the difference between the INS-and UWB-based distance measurements.The main filter produces a final optimal estimate of the human position by fusing the estimates from local filters.The effect of CMN is overcome by using measurement differencing of noisy observations.The tests show that the proposed dKF developed for CMN with CFM can reduce the localization error compared to the original dKF,and thus effectively improve the localization accuracy.

Non-Gaussian noise-enhanced stochastic rate oscillations in CO oxidation on nanometer-sized Pd particles

The effect of non-Gaussian colored noise(NGN),mainly its departure q from the Gaussian noise,on the optimal ISRO of CO oxidation on nanometer-sized Pd particles was studied.It was found that the ISRO in the absence of external noise can still be enhanced when the NGN is applied.Specifically,the ISRO varies with changing q and becomes more regular at an appropriate q value,and when q is optimal,the ISRO becomes the most regular.Because the departure q from the Gaussian noise determines the probability distribution function and hence may denote the types of noise,this result shows that different types of external noise can enhance the ISRO of CO oxidation,and non-Gaussian noise may enhance the ISRO more greatly than the Gaussian noise.Therefore,non-Gaussian noise could play more effective roles in the catalytic process of CO oxidation on nanometer-sized Pd particles.

Stabilizability of minimum-phase systems with colored multiplicative uncertainty

This work addresses the mean-square stability and stabilizability problem for minimum-phase multi-input and multi-output(MIMO)plant with a novel colored multiplicative feedback uncertainty.The proposed uncertainty is generalization of the i.i.d.multiplicative noise and assumed to be a stochastic system with random finite impulse response(FIR),which has advantage on modeling a class of network phenomena such as random transmission delays.A concept of coefficient of frequency variation is developed to characterize the proposed uncertainty.Then,the mean-square stability for the system is derived,which is a generalization of the well-known mean-square small gain theorem.Based on this,the mean-square stabilizability condition is established,which reveals the inherent connection between the stabilizability and the plant’s unstable poles and the coefficient of frequency variation of the uncertainty.The result is verified by a numerical example on the stabilizability of a networked system with random transmission delay as well as analog erasure channel.

Probabilistic description of extreme oscillations and reliability analysis in rolling motion under stochastic excitation

Large-amplitude rolling motions, also regarded as extreme oscillations, are a great threat to marine navigation, which may lead to capsizing in ship motion. Therefore, it is important to quantify extreme oscillations, assess reliability of ship systems, and establish a suitable indicator to characterize extreme oscillations in ship systems. In this work, extreme events are investigated in a ship model considering a complex ocean environment, described by a single-degree-of-freedom nonlinear system with stochastic harmonic excitation and colored Gaussian noise. The stationary probability density function(PDF) of the system is derived through a probabilistic decomposition-synthesis method. Based on this, we infer the classical damage rate of the system. Furthermore, a new indicator, independent of the PDF, is proposed to quantify the damage related only to the fourth-order moment of the system and the threshold for extreme events. It is more universal and easier to determine as compared with the classical damage rate. A large damping ratio, a large noise intensity, or a short correlation time can reduce the damage rate and the value of the indicator.These findings provide new insights and theoretical guidance to avoid extreme oscillations and assess the reliability of practical ship movements.