Dynamical behavior of a tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the a...Dynamical behavior of a tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the active state, induce the minimum of the average tumor-cell population to move toward a smaller non-Gaussian noise, but also decrease the mean first-passage time. The increase of white-noise intensity can increase the tumor-cell population and shorten the mean first-passage time, while the coupling strength between noise terms has opposite effects, and the noise correlation time has a very small effect.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
Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non...Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.展开更多
A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transforma...A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon's information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.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
In this paper, a general method of synchronizing noise-perturbed chaotic systems with unknown parameters is proposed. Based on the LaSalle-type invariance principle for stochastic differential equations and by employi...In this paper, a general method of synchronizing noise-perturbed chaotic systems with unknown parameters is proposed. Based on the LaSalle-type invariance principle for stochastic differential equations and by employing a combination of feedback control and adaptive control, some sufficient conditions of chaos synchronization between these noise-perturbed systems with unknown parameters are established. The model used in the research is the chaotic system, but the method is also applicable to the hyperchaotic systems. Unified system and noise-perturbed RSssler system, hyperchaotic Chen system and nolse-perturbed hyperchaotic RSssler system are taken for illustrative examples to demonstrate this technique.展开更多
A single-mode laser system with non-Gaussian and Gaussian noise is investigated. The stationary mean value and the normalized variance of the laser intensity are numerically calculated under the condition that the sta...A single-mode laser system with non-Gaussian and Gaussian noise is investigated. The stationary mean value and the normalized variance of the laser intensity are numerically calculated under the condition that the stationary probability distribution function (SPDF) is derived. The SPDF as a function of the laser intensity exhibits a maximum, The maximum becomes smaller with the increase of the correlation intensity or the non-Gaussian parameter, where the later is a measure of the deviation from the Gaussian characteristic. The maximum becomes larger as the correlation time increases. The laser intensity stationary mean value decreases with the increase of the correlation intensity or the non-Gaussian parameter while increases with the correlation time increasing. The laser intensity normalized variance increases with the increase of the correlation intensity or the non-Gaussian parameter while decreases as the correlation time increases.展开更多
This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels sub...This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.展开更多
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis ...Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.展开更多
We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum (Rmax) with i...We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum (Rmax) with increasing noise intensity Q. The non-Gaussian noise parameter q has an important effect on the system. For some values of q (e.g., q = 0.9, q = 1.0), R has a maximum with increasing correlation time t. Non-Gaussian noise induced spikes are more regular than Gaussian noise induced spikes when q is small and Q has large values. The R has a maximum with increasing q. Therefore, non-Gaussian noise could play more effective roles in the calcium oscillation system.展开更多
The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non- Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the sta...The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non- Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the stationary properties and the transient properties are discussed, respectively. The results show that the nonextensive index q can induce the tumor cell numbers to decrease greatly in the case of q 〉 1. Moreover, the switch from the steady stable state to the extinct state is speeded up as the increases of q, and the tumor cell numbers can be more obviously restrained for a large value of q. The numerical results are found to be in basic agreement with the theoretical predictions.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
In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C(t) of the n...In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C(t) of the non-Gaussian stochastic process,and find that they depend on the parameter q,indicating the departure of the non-Gaussian noise from Gaussian behavior:for q ≤ 1,C(t) is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit,whereas for q 〉 1,C(t) can be approximated by a second-order exponentially decaying function and converges to a non-zero constant.Due to the properties of C(t),the particle exhibits a normal diffusion for q ≤ 1,while for q 〉 1 the non-Gaussian noise induces a ballistic diffusion,i.e.,the long-time mean square displacement of the free particle reads 〈[x(t)-]2∝t2.展开更多
This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs ...This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.展开更多
This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take ...This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic variables. To enhance the “robustness” of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate. By taking advantage of an upper bound on the one-step prediction error covariance, a modified MCC-based performance index is constructed. Subsequently, with the assistance of a fixed-point theorem, the filter gain is obtained by maximizing the proposed cost function. In addition, a sufficient condition is deduced to ensure the uniqueness of the fixed point. Finally, the validity of the filtering method is tested by simulating a numerical example.展开更多
This paper addresses the harmonic retrieval problem in non-Gaussian ARMA noise. A hybrid ESPRIT approach using second-and third-order statistics is proposed. First, third-order statistics are used to identify the AR p...This paper addresses the harmonic retrieval problem in non-Gaussian ARMA noise. A hybrid ESPRIT approach using second-and third-order statistics is proposed. First, third-order statistics are used to identify the AR part of the non-Gaussian noise process, then the noisy measurements are filtered by AR polynomial, finally, the harmonic signal parameters are estimated. Simulation examples show the effectiveness and high resolution of the new approach.展开更多
Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to...Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.展开更多
Glitches represent a category of non-Gaussian and transient noise that frequently intersects with gravitational wave(GW)signals,thereby exerting a notable impact on the processing of GW data.The inference of GW parame...Glitches represent a category of non-Gaussian and transient noise that frequently intersects with gravitational wave(GW)signals,thereby exerting a notable impact on the processing of GW data.The inference of GW parameters,crucial for GW astronomy research,is particularly susceptible to such interference.In this study,we pioneer the utilization of a temporal and time-spectral fusion normalizing flow for likelihood-free inference of GW parameters,seamlessly integrating the high temporal resolution of the time domain with the frequency separation characteristics of both time and frequency domains.Remarkably,our findings indicate that the accuracy of this inference method is comparable to that of traditional non-glitch sampling techniques.Furthermore,our approach exhibits a greater efficiency,boasting processing times on the order of milliseconds.In conclusion,the application of a normalizing flow emerges as pivotal in handling GW signals affected by transient noises,offering a promising avenue for enhancing the field of GW astronomy research.展开更多
During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditi...During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density (PSD), skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11005077, 11105095, and 11074184)the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province, China (Grant No. 10KJD140003)
文摘Dynamical behavior of a tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the active state, induce the minimum of the average tumor-cell population to move toward a smaller non-Gaussian noise, but also decrease the mean first-passage time. The increase of white-noise intensity can increase the tumor-cell population and shorten the mean first-passage time, while the coupling strength between noise terms has opposite effects, and the noise correlation time has a very small effect.
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.
基金the National Natural Science Foundation of China(No.12072118)the Natural Science Funds for Distinguished Young Scholar of Fujian Province of China(No.2021J06024)the Project for Youth Innovation Fund of Xiamen of China(No.3502Z20206005)。
文摘Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10872165)
文摘A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated. The Fokker Plank equation of the system is obtained through the path-integral approach and the method of transformation. Based on the definition of Shannon's information entropy and the Schwartz inequality principle, the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculations can be used to interpret the effects of the system dissipative parameter, the system singularity strength parameter, the noise correlation time and the noise deviation parameter on the upper bound.
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Project supported by the National Natural Science Foundation of China (Grant Nos 10472091 and 10332030) and the Graduate Starting Seed Fund of Northwestern Polytechnical University, China (Grant No Z200655).
文摘In this paper, a general method of synchronizing noise-perturbed chaotic systems with unknown parameters is proposed. Based on the LaSalle-type invariance principle for stochastic differential equations and by employing a combination of feedback control and adaptive control, some sufficient conditions of chaos synchronization between these noise-perturbed systems with unknown parameters are established. The model used in the research is the chaotic system, but the method is also applicable to the hyperchaotic systems. Unified system and noise-perturbed RSssler system, hyperchaotic Chen system and nolse-perturbed hyperchaotic RSssler system are taken for illustrative examples to demonstrate this technique.
文摘A single-mode laser system with non-Gaussian and Gaussian noise is investigated. The stationary mean value and the normalized variance of the laser intensity are numerically calculated under the condition that the stationary probability distribution function (SPDF) is derived. The SPDF as a function of the laser intensity exhibits a maximum, The maximum becomes smaller with the increase of the correlation intensity or the non-Gaussian parameter, where the later is a measure of the deviation from the Gaussian characteristic. The maximum becomes larger as the correlation time increases. The laser intensity stationary mean value decreases with the increase of the correlation intensity or the non-Gaussian parameter while increases with the correlation time increasing. The laser intensity normalized variance increases with the increase of the correlation intensity or the non-Gaussian parameter while decreases as the correlation time increases.
基金the support of SNCS Research Center and the Deanship of Scientific Research at the University of Tabukfinancial and inkind support for the project no. S-1438-0161
文摘This paper derives new and exact closed-form expressions for the average symbol error rate(SER) of square M-ary quadrature amplitude modulation(M-QAM) in wireless communication systems over theα-μfading channels subject to an additive non-Gaussian noise. The obtained expressions take into account static and mobile wireless receivers. In addition, a closed-form expression for the outage probability in mobile networks is obtained. Please note that all derived expressions in this paper a valid for integer and non-integer values of the fading parameters. Analytical results are presented to study the impact of noise shaping parameter, severity of fading, and mobility on the average SER. Monte-Carlo simulations results are also provided to validate the accuracy of the analytical results.
基金supported by the NSFC(10971225, 11171125, 91130003 and 11028102)the NSFH (2011CDB289)+1 种基金HPDEP (20114503 and 2011B400)the Cheung Kong Scholars Program and the Fundamental Research Funds for the Central Universities, HUST(2010ZD037)
文摘Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises.
基金Project supported by the Natural Science Foundation of Anhui Province, China (Grant No. KJ2012A085)
文摘We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum (Rmax) with increasing noise intensity Q. The non-Gaussian noise parameter q has an important effect on the system. For some values of q (e.g., q = 0.9, q = 1.0), R has a maximum with increasing correlation time t. Non-Gaussian noise induced spikes are more regular than Gaussian noise induced spikes when q is small and Q has large values. The R has a maximum with increasing q. Therefore, non-Gaussian noise could play more effective roles in the calcium oscillation system.
基金supported by the National Natural Science Foundation of China (Grant No. 11205006)the Science Foundation of the Education Bureau of Shaanxi Province, China (Grant No. 12JK0962)the Science Foundation of Baoji University of Arts and Sciences of China (Grant No. ZK11053)
文摘The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non- Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the stationary properties and the transient properties are discussed, respectively. The results show that the nonextensive index q can induce the tumor cell numbers to decrease greatly in the case of q 〉 1. Moreover, the switch from the steady stable state to the extinct state is speeded up as the increases of q, and the tumor cell numbers can be more obviously restrained for a large value of q. The numerical results are found to be in basic agreement with the theoretical predictions.
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 Research Start-up Foundation for Young Teachers of Northwest A&F University of China (Grant No. Z111020904)
文摘In this letter,we have analyzed the diffusive behavior of a Brownian particle subject to both internal Gaussian thermal and external non-Gaussian noise sources.We discuss two time correlation functions C(t) of the non-Gaussian stochastic process,and find that they depend on the parameter q,indicating the departure of the non-Gaussian noise from Gaussian behavior:for q ≤ 1,C(t) is fitted very well by the first-order exponentially decaying curve and approaches zero in the longtime limit,whereas for q 〉 1,C(t) can be approximated by a second-order exponentially decaying function and converges to a non-zero constant.Due to the properties of C(t),the particle exhibits a normal diffusion for q ≤ 1,while for q 〉 1 the non-Gaussian noise induces a ballistic diffusion,i.e.,the long-time mean square displacement of the free particle reads 〈[x(t)-]2∝t2.
基金This work was supported in part by National Natural Science Foundation of China under Grants 62103167 and 61833007in part by the Natural Science Foundation of Jiangsu Province under Grant BK20210451.
文摘This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.
基金supported in part by the National Natural Science Foundation of China (62273088, 62273087)the Shanghai Pujiang Program of China (22PJ1400400)the Program of Shanghai Academic/Technology Research Leader (20XD1420100)。
文摘This paper tackles the maximum correntropy Kalman filtering problem for discrete time-varying non-Gaussian systems subject to state saturations and stochastic nonlinearities. The stochastic nonlinearities, which take the form of statemultiplicative noises, are introduced in systems to describe the phenomenon of nonlinear disturbances. To resist non-Gaussian noises, we consider a new performance index called maximum correntropy criterion(MCC) which describes the similarity between two stochastic variables. To enhance the “robustness” of the kernel parameter selection on the resultant filtering performance, the Cauchy kernel function is adopted to calculate the corresponding correntropy. The goal of this paper is to design a Kalman-type filter for the underlying systems via maximizing the correntropy between the system state and its estimate. By taking advantage of an upper bound on the one-step prediction error covariance, a modified MCC-based performance index is constructed. Subsequently, with the assistance of a fixed-point theorem, the filter gain is obtained by maximizing the proposed cost function. In addition, a sufficient condition is deduced to ensure the uniqueness of the fixed point. Finally, the validity of the filtering method is tested by simulating a numerical example.
文摘This paper addresses the harmonic retrieval problem in non-Gaussian ARMA noise. A hybrid ESPRIT approach using second-and third-order statistics is proposed. First, third-order statistics are used to identify the AR part of the non-Gaussian noise process, then the noisy measurements are filtered by AR polynomial, finally, the harmonic signal parameters are estimated. Simulation examples show the effectiveness and high resolution of the new approach.
基金Supported in part by the NNSF of China(11301129,11271323,91330105,11326033)the Zhejiang Provincial Natural Science Foundation of China(LQ13A010025,LZ13A010002)
文摘Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others, these results show that our proposed model and algorithms are effective.
基金the National SKA Program of China(2022SKA0110200,2022SKA0110203)the National Natural Science Foundation of China(11975072,11875102,11835009)the National 111 Project(B16009)。
文摘Glitches represent a category of non-Gaussian and transient noise that frequently intersects with gravitational wave(GW)signals,thereby exerting a notable impact on the processing of GW data.The inference of GW parameters,crucial for GW astronomy research,is particularly susceptible to such interference.In this study,we pioneer the utilization of a temporal and time-spectral fusion normalizing flow for likelihood-free inference of GW parameters,seamlessly integrating the high temporal resolution of the time domain with the frequency separation characteristics of both time and frequency domains.Remarkably,our findings indicate that the accuracy of this inference method is comparable to that of traditional non-glitch sampling techniques.Furthermore,our approach exhibits a greater efficiency,boasting processing times on the order of milliseconds.In conclusion,the application of a normalizing flow emerges as pivotal in handling GW signals affected by transient noises,offering a promising avenue for enhancing the field of GW astronomy research.
文摘During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density (PSD), skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal