We investigate the stochastic resonance (SR) phenomenon induced by the periodic signal in a metapopulation system with colored noises. The analytical expression of signal-to-noise is derived in the adiabatic limit. ...We investigate the stochastic resonance (SR) phenomenon induced by the periodic signal in a metapopulation system with colored noises. The analytical expression of signal-to-noise is derived in the adiabatic limit. By numerical calculation, the effects of the addictive noise intensity, the multiplicative noise intensity and two noise self-correlation times on SNR are respectively discussed. It shows that: (i) in the case that the addictive noise intensity M takes a small value, a SR phenomenon for the curve of SNR appears; however, when M takes a large value, SNR turns into a monotonic function on the multiplicative noise intensity Q. (ii) The resonance peaks in the plots of the multiplicative noise intensity Q versus its self-correlation time Vl and the addictive noise intensity M versus its self-correlation time ~2 translate in parallel. Mean- while, a parallel translation also appears in the plots of vl versus Q and v2 versus M. (iii) The interactive effects between self-correlation times Vl and v2 are opposite.展开更多
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-re...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.展开更多
We investigate a wave equation in the plane with an additive noise which is fractional in time and has a non-degenerate spatial covariance. The equation is shown to admit a process-valued solution. Also we give a cont...We investigate a wave equation in the plane with an additive noise which is fractional in time and has a non-degenerate spatial covariance. The equation is shown to admit a process-valued solution. Also we give a continuity modulus of the solution, and the HSlder continuity is presented.展开更多
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-de...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.展开更多
A multiple targets detection method based on spatial smoothing (MTDSS) is proposed to solve the problem of the source number estimation under the colored noise background. The forward and backward smoothing based on...A multiple targets detection method based on spatial smoothing (MTDSS) is proposed to solve the problem of the source number estimation under the colored noise background. The forward and backward smoothing based on auxiliary vectors which are received data on some specific elements is computed. By the spatial smoothing with auxiliary vectors, the correlated signals are decorrelated, and the colored noise is partially alleviated. The correlation matrix formed from the cross correlations between subarray data and auxiliary vectors is computed. By exploring the second-order statistics property of the covariance matrix, a threshold based on Gerschgorin radii of the smoothing correlation matrix is set to estimate the number of sources. Simulations and experimental results validate that MTDSS has an effective performance under the condition of the colored noise background and coherent sources, and MTDSS is robust with the correlated factor of signals and noise.展开更多
A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the h...A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function (PDF) of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.展开更多
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-pa...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.展开更多
Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in t...Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio ?t/(1/λ) where ?t is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time ?t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio ?t/(1/λ) is less than 1, the uncertainty remains substantially unchanged.展开更多
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 ...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.展开更多
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 portra...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.展开更多
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 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.展开更多
The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper. According to the Fokker-Planck equation in the unified colored-noise approximation...The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper. According to the Fokker-Planck equation in the unified colored-noise approximation, we analyse the stationary probability distribution and the mean first-passage time of this model. By numerical analysis, the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density. The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.展开更多
The approach of estimating the number of signals based on information theoretic criteria has good performance in the assumption of white noise, but it always leads to false estimation of the coherent sources in colore...The approach of estimating the number of signals based on information theoretic criteria has good performance in the assumption of white noise, but it always leads to false estimation of the coherent sources in colored noise. An approach combining the combined information theoretic criteria and eigen- value correction, is presented to determine number of signals. The method uses maximum likelihood (ML) and information theoretic criteria to estimate coherent signals alternately, then eliminate the inequality of the eigenvalues caused by colored noise by correcting the noise eigenvalues. The computer simulation results prove the effective performance of the method.展开更多
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 ma...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.展开更多
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 c...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.展开更多
A new variable step-size algorithm for a second-order lattice form structure adaptive infinite impulse response (IIR) notch filter to detection and estimation frequency of sinusoids in Gaussian noises is proposed. U...A new variable step-size algorithm for a second-order lattice form structure adaptive infinite impulse response (IIR) notch filter to detection and estimation frequency of sinusoids in Gaussian noises is proposed. Utilizing least square kurtosis of output signals as a cost function, the new gradient-based algorithm to update frequency of the adaptive IIR notch filter and the new variable step-size algorithm are given. The computer simulation results show that the proposed algorithm has better ability in suppressing colored Gaussian noises and better accuracy in estimating parameters at low SNR than previous algorithms.展开更多
The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed int...The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.展开更多
This paper addresses the problem of four-dimensional angle and Doppler frequency estimation for bistatic multiple-input multiple-output (MIMO) radar with arbitrary arrays in spatial co- lored noise. A novel method f...This paper addresses the problem of four-dimensional angle and Doppler frequency estimation for bistatic multiple-input multiple-output (MIMO) radar with arbitrary arrays in spatial co- lored noise. A novel method for joint estimation of Doppler fre- quency, two-dimensional (2D) direction of departure and 2D direc- tion of arrival based on the propagator method (PM) for arbitrary arrays is discussed. A special matrix is constructed to eliminate the influence of spatial colored noise. The four-dimensional (4D) angle and Doppler frequency are extracted from the matrix and the three- dimensional (3D) coordinates of the targets are then calculated on the basis of these angles. The proposed algorithm provides a lower computational complexity and has a parameter estimation very close to that of the ESPRIT algorithm and the DOA-matrix al- gorithm in the high signal to noise ratio and the Cramer-Rao bound (CRB) is given. Furthermore, multi-dimensional parameters can be automatically paired by this algorithm to avoid performance degra- dation resulting from wrong pairing. Simulation results demonstrate the effectiveness of the proposed method.展开更多
The precision of Earth's gravitational field from GRACE up to degree and order 120 was studied for different inter-satellite ranges using the improved energy conservation principle. Our simulated result shows that: ...The precision of Earth's gravitational field from GRACE up to degree and order 120 was studied for different inter-satellite ranges using the improved energy conservation principle. Our simulated result shows that: For long wavelength (L≤20) at degree 20, the cumulative geoid-height error gradually decreased with increasing range, from 0. 052 cm for 110 km to 1. 156 times and 1. 209 times as large for 220 km and 330 kin, respectively. For medium-wavelength ( 100 ≤ L ≤ 120) at degree 120, the cumulative geoid-height error de- creased from 13. 052 cm for 110 km, to 1. 327 times and 1. 970 times as large for the ranges of 220 km and 330 km, respectively; By adopting an optimal range of 220 ± 50 km, we can suppress considerably the loss of precision in the measurement of the Earth' s long-wavelength and medium-wavelength gravitational field.展开更多
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 i...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.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11072107,91016022,and 11232007)the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures of Nanjing University of Aeronautics and astronautics,China(Grant No.0113G01)+1 种基金the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,China(Grant No.13KJB110006)the Project Fund of Jiangsu University of Science and Technology,China(Grant No.633051203)
文摘We investigate the stochastic resonance (SR) phenomenon induced by the periodic signal in a metapopulation system with colored noises. The analytical expression of signal-to-noise is derived in the adiabatic limit. By numerical calculation, the effects of the addictive noise intensity, the multiplicative noise intensity and two noise self-correlation times on SNR are respectively discussed. It shows that: (i) in the case that the addictive noise intensity M takes a small value, a SR phenomenon for the curve of SNR appears; however, when M takes a large value, SNR turns into a monotonic function on the multiplicative noise intensity Q. (ii) The resonance peaks in the plots of the multiplicative noise intensity Q versus its self-correlation time Vl and the addictive noise intensity M versus its self-correlation time ~2 translate in parallel. Mean- while, a parallel translation also appears in the plots of vl versus Q and v2 versus M. (iii) The interactive effects between self-correlation times Vl and v2 are opposite.
基金supported in part by the Open Research Funds of BACC-STAFDL of China under Grant No.2015afdl010the National Natural Science Foundation of China under Grant No.61673282the PCSIRT16R53
文摘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.
基金Supported by NationalNatural Science Foundation of China (Grant No. 10871103)
文摘We investigate a wave equation in the plane with an additive noise which is fractional in time and has a non-degenerate spatial covariance. The equation is shown to admit a process-valued solution. Also we give a continuity modulus of the solution, and the HSlder continuity is presented.
基金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)+1 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.JB160706)Chinese–Serbian Science and Technology Cooperation for the Years 2015-2016(Grant No.3-19)
文摘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.
基金supported by the National Natural Science Foundation of China (61001153)the Fundamental Research Program of Northwestern Polytechnical University (JC20100223)
文摘A multiple targets detection method based on spatial smoothing (MTDSS) is proposed to solve the problem of the source number estimation under the colored noise background. The forward and backward smoothing based on auxiliary vectors which are received data on some specific elements is computed. By the spatial smoothing with auxiliary vectors, the correlated signals are decorrelated, and the colored noise is partially alleviated. The correlation matrix formed from the cross correlations between subarray data and auxiliary vectors is computed. By exploring the second-order statistics property of the covariance matrix, a threshold based on Gerschgorin radii of the smoothing correlation matrix is set to estimate the number of sources. Simulations and experimental results validate that MTDSS has an effective performance under the condition of the colored noise background and coherent sources, and MTDSS is robust with the correlated factor of signals and noise.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11172233,10932009,and 11202160)the Natural Science Foundation of Shaanxi Province,China(Grant No.2012JQ1004)
文摘A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function (PDF) of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored.
基金Project supported by the National Natural Science Foundation of China(Grant No.60551002)the Natural Science Foundation of Hunan Province,China(Grant No.2018JJ3680).
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175160,11275075,and 11575160)
文摘Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio ?t/(1/λ) where ?t is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time ?t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio ?t/(1/λ) is less than 1, the uncertainty remains substantially unchanged.
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11902081)the Science and Technology Innovation Foundation of Higher Education Institutions of Shanxi Province,China(Grant No.2020L0172)+1 种基金the Natural Science Foundation for Young Scientists of Shanxi Agricultural University,China(Grant No.2020QC04)the Research Fund of Shanxi Agriculture University,China(Grant No.2021BQ12)。
文摘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.
基金Project supported by the Natural Science Basic Research Plan in Shaanxi Province,China (Grant No. SJ08A12)the Science Foundation of the Education Bureau of Shaanxi Province,China (Grant No. 12JK0962)the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK11053)
文摘The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper. According to the Fokker-Planck equation in the unified colored-noise approximation, we analyse the stationary probability distribution and the mean first-passage time of this model. By numerical analysis, the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density. The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.
文摘The approach of estimating the number of signals based on information theoretic criteria has good performance in the assumption of white noise, but it always leads to false estimation of the coherent sources in colored noise. An approach combining the combined information theoretic criteria and eigen- value correction, is presented to determine number of signals. The method uses maximum likelihood (ML) and information theoretic criteria to estimate coherent signals alternately, then eliminate the inequality of the eigenvalues caused by colored noise by correcting the noise eigenvalues. The computer simulation results prove the effective performance of the method.
基金Strategic Priority Research Program of Chinese Academy of Sciences,Grant No.XDA28040000,XDA28120000Natural Science Foundation of Shandong Province,Grant No.ZR2021MF094+2 种基金Key R&D Plan of Shandong Province,Grant No.2020CXGC010804Central Leading Local Science and Technology Development Special Fund Project,Grant No.YDZX2021122Science&Technology Specific Projects in Agricultural High-tech Industrial Demonstration Area of the Yellow River Delta,Grant No.2022SZX11。
文摘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.
基金CMMI 1760366 and the as-sociated data science supplementsA preliminary report of this work has been presented and discussed at the ASME 2022 Inter-national Design Engineering Technical Conference&Computer and Information in Engineering conference(IDETC/CIE 2022)。
文摘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.
文摘A new variable step-size algorithm for a second-order lattice form structure adaptive infinite impulse response (IIR) notch filter to detection and estimation frequency of sinusoids in Gaussian noises is proposed. Utilizing least square kurtosis of output signals as a cost function, the new gradient-based algorithm to update frequency of the adaptive IIR notch filter and the new variable step-size algorithm are given. The computer simulation results show that the proposed algorithm has better ability in suppressing colored Gaussian noises and better accuracy in estimating parameters at low SNR than previous algorithms.
基金the Foundation of ECUST(East China University of Science and Technology)for Outstanding Young Teachers(YH0157105)
文摘The first-passage statistics of Duffing-Rayleigh- Mathieu system under wide-band colored noise excitations is studied by using stochastic averaging method. The motion equation of the original system is transformed into two time homogeneous diffusion Markovian processes of amplitude and phase after stochastic averaging. The diffusion process method for first-passage problem is used and the corresponding backward Kolmogorov equation and Pontryagin equation are constructed and solved to yield the conditional reliability function and mean first-passage time with suitable initial and boundary conditions. The analytical results are confirmed by Monte Carlo simulation.
基金supported by the National Natural Science Foundation of China(6137116961179006)+1 种基金the Jiangsu Postdoctoral Research Funding Plan(1301013B)the Nanjing University of Aeronautics and Astronautics Funding(NZ2013208)
文摘This paper addresses the problem of four-dimensional angle and Doppler frequency estimation for bistatic multiple-input multiple-output (MIMO) radar with arbitrary arrays in spatial co- lored noise. A novel method for joint estimation of Doppler fre- quency, two-dimensional (2D) direction of departure and 2D direc- tion of arrival based on the propagator method (PM) for arbitrary arrays is discussed. A special matrix is constructed to eliminate the influence of spatial colored noise. The four-dimensional (4D) angle and Doppler frequency are extracted from the matrix and the three- dimensional (3D) coordinates of the targets are then calculated on the basis of these angles. The proposed algorithm provides a lower computational complexity and has a parameter estimation very close to that of the ESPRIT algorithm and the DOA-matrix al- gorithm in the high signal to noise ratio and the Cramer-Rao bound (CRB) is given. Furthermore, multi-dimensional parameters can be automatically paired by this algorithm to avoid performance degra- dation resulting from wrong pairing. Simulation results demonstrate the effectiveness of the proposed method.
基金supported by the Main Direction Program of Knowledge Innovation of Chinese Academy of Sciences for Distinguished Young Scholar(KZCX2-EW-QN114)the National Natural Science Foundation of China(41004006,41131067,11173049)+5 种基金the Merit-based Scientific Research Foundation of the State Ministry of Human Resources and Social Security of China for Returned Overseas Chinese Scholars(2011)the Open Research Fund Program of the Key Laboratory of Geo-Informatics of State Bureau of Surveying and Mapping(201031)the Open Research Fund Program of the Key Laboratory of Computational Geodynamics of Chinese Academy of Sciences(2011-04)the Frontier Field Program of Knowledge Innovation of Institute of Geodesy and Geophysics of Chinese Academy of Sciencesthe Open Fund of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(PLN1113)the Hubei Province Key Laboratory of Refractories and Ceramics Ministry-Province jointly-Constructed Cultivation Base for State key Laboratory(G201009)
文摘The precision of Earth's gravitational field from GRACE up to degree and order 120 was studied for different inter-satellite ranges using the improved energy conservation principle. Our simulated result shows that: For long wavelength (L≤20) at degree 20, the cumulative geoid-height error gradually decreased with increasing range, from 0. 052 cm for 110 km to 1. 156 times and 1. 209 times as large for 220 km and 330 kin, respectively. For medium-wavelength ( 100 ≤ L ≤ 120) at degree 120, the cumulative geoid-height error de- creased from 13. 052 cm for 110 km, to 1. 327 times and 1. 970 times as large for the ranges of 220 km and 330 km, respectively; By adopting an optimal range of 220 ± 50 km, we can suppress considerably the loss of precision in the measurement of the Earth' s long-wavelength and medium-wavelength gravitational field.
基金the National Natural Science Foundation of China(Nos.61701046,61871218 and 62071476).
文摘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.