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1.
The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the
infinitely divisible distribution of the Lévy process we study the nonlinear relaxation of the population density for three
cases of white non-Gaussian noise: (i) shot noise; (ii) noise with a probability density of increments expressed in terms
of Gamma function; and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population
density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover
starting from an initial delta function distribution, we find a transition induced by the multiplicative Lévy noise, from
a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior
of the nonlinear relaxation time as a function of the Cauchy stable noise intensity. 相似文献
2.
We construct complex networks from lévy noise (LN) using visibility algorithm proposed by Lucas lacasa el al. It is found that as the stability index α of the symmetric LN decreases, the corresponding complex network will transit from exponential network to long-tailed-degree-distribution
one, and then to Gaussian one. The associated network for symmetric LN is the high clustering, hierarchy, and 18 community
network. The properties of the associated networks for asymmetric LN except the skewness parameter β = −1 are similar with that for symmetric one. The associated network for the asymmetric LN with the skewness parameter β = −1 is always the exponential, high clustering, and hierarchy one with small k-clique communities. 相似文献
3.
Stochastic motion in a bistable, periodically modulated potential is discussed. Thesystem is stimulated by a white noise increments of which have a symmetric stable Lévydistribution. The noise is multiplicative: its intensity depends on the process variablelike | x| ?θ . The Stratonovich and Itôinterpretations of the stochastic integral are taken into account. The mean first passagetime is calculated as a function of θ for different values of thestability index α and size of the barrier. Dependence of the outputamplitude on the noise intensity reveals a pattern typical for the stochastic resonance.Properties of the resonance as a function of α, θ andsize of the barrier are discussed. Both height and position of the peak strongly dependson θ and on a specific interpretation of the stochastic integral. 相似文献
4.
In this paper, we investigate the effect of alpha stable Lévy noise with alpha stability index α ( ) on stochastic resonance (SR) in underdamped periodic potential systems by the non-perturbative expansion moment method and stochastic simulation. Using the spectral amplification factor as a quantifying index, we find that SR can occur in both sinusoidal potentials and ratchet potentials when α is close to 2, while the resonant effect becomes weaker as the stability index decreases. By means of massive numerical statistics, we ascribe this trend to the typical jumps of non-Gaussian Lévy noise ( ), which play a destructive role on the periodicity of the long time mean response. We also disclose that the skewness parameter of Lévy noise has a more notable impact on the resonant effect of the asymmetric ratchet potential than that of the symmetric sinusoidal potential because of symmetry breaking. 相似文献
5.
In the past few years, attention has mainly been focused on the symmetric Brownian motor(BM) with Gaussian noises, whose current and energy conversion efficiency are very low. Here, we investigate the operating performance of the symmetric BM subjected to Lévy noise. Through numerical simulations, it is found that the operating performance of the motor can be greatly improved in asymmetric Lévy noise. Without any load, the Lévy noises with smaller stable indexes can let the motor give rise to a ... 相似文献
6.
In this paper, we calculate the localization length of a TM electromagnetic wave in unitof system length versus incident angle in a disordered layered structure where therefractive index of one of its constituents follows a Lévy-type distribution with a powerexponent α.The incident angle at which the localization length takes the maximum value is called thegeneralized Brewster angle as before. However, in contrast to previous works with a weakdisorder, the wave incident at generalized Brewster angle is not always in the extendedregime. For special values of α and the frequency, the system is in a localizedstate at this angle. But, the localization length at this Brewster angle is always largerthan that at other angles. The effects of α variation on the localization length at thisBrewster angle and its position are investigated for different frequencies. Thelocalization at this angle degrades with increasing α for all frequencies. Atsome working frequencies, the generalized Brewster angle is a decreasing function of α. However,at other frequencies, the dependence of generalized Brewster angle on α is not monotonic. Forincident angles smaller than a specific angle, the localization length increases withincreasing α.However, for incident angles larger than this specific angle, there are incident angles atwhich any increase of α leads to the decrease of localization length. Inother words, for these incident angles, the improvement of Anderson localizationsurprisingly happens with decrease of disorder strength and the refractive index contrast. 相似文献
7.
We propose a scheme to generate the Greenberger-Horne-Zeilinger (GHZ) states and the cluster states of many trapped ions. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed, which is important in view of decoherence. 相似文献
8.
We investigate the problem of ■ state estimation for discrete-time Markov jump neural networks. The transition probabilities of the Markov chain are assumed to be piecewise time-varying, and the persistent dwell-time switching rule,as a more general switching rule, is adopted to describe this variation characteristic. Afterwards, based on the classical Lyapunov stability theory, a Lyapunov function is established, in which the information about the Markov jump feature of the system mode and the persistent dwell-time switching of the transition probabilities is considered simultaneously.Furthermore, via using the stochastic analysis method and some advanced matrix transformation techniques, some sufficient conditions are obtained such that the estimation error system is mean-square exponentially stable with an ■ performance level, from which the specific form of the estimator can be obtained. Finally, the rationality and effectiveness of the obtained results are verified by a numerical example. 相似文献
9.
From the evolutionary vector deacription of slowly sime-varyingnoise process,a measure for non-stationarity is developed.It includesboth the non-stationarities of power and of spectrum shape.As a singleparameter,it is a comparable quantity for different processes.Applicationto the analysis of precise gearbox is prescnted. 相似文献
10.
We study the properties of the probability density function (PDF) of a bistable system driven by heavy tailed white symmetric Lévy noise. The shape of the stationary PDF is found analytically for the particular case of the Lévy index α = 1 (Cauchy noise). For an arbitrary Lévy index we employ numerical methods based on the solution of the stochastic Langevin equation and space fractional kinetic equation. In contrast to the bistable system driven by Gaussian noise, in the Lévy case, the positions of maxima of the stationary PDF do not coincide with the positions of minima of the bistable potential. We provide a detailed study of the distance between the maxima and the minima as a function of the depth of the potential and the Lévy noise parameters. 相似文献
11.
In this paper, the stochastic resonance (SR) of a multi-stable system driven by Lévy noise is investigated by the mean signal-to-noise ratio gain (SNR-GM). The characteristics for resonant output of multi-stable system, governed by the system parameters ( a and c), the noise amplification factor D of Lévy noise are investigated under different values of stability index α and asymmetry parameter β of Lévy noise. The results reveal that the parameter α is closer to 1, the amplitude of SNR-GM versus system parameter a (or c) is larger. The interval of SR presents a trend that the curve of SNR-GM shifts to the right with the increase of α especially when α > 1. In addition, the SNR-GM for different values of system parameter a (or c) exhibits a tendency to move to the left with the increase of system parameter c (or a). Finally, the simulation results prove that the proposed multi-stable model has better advantage than bistable system and monostable system in signal enhancement and SNR-GM performance. 相似文献
12.
We investigate the problem of H∞ state estimation for discrete-time Markov jump neural networks.The transition probabilities of the Markov chain are assumed to ... 相似文献
13.
Using the data on the Berlin public transport network, the present study extends previous observations of fractality within public transport routes by showing that also the distribution of inter-station distances along routes displays non-trivial power law behaviour. This indicates that the routes may in part also be described as Lévy-flights. The latter property may result from the fact that the routes are planned to be adapted to the fluctuating demand densities throughout the served area. We also relate this to optimization properties of Lévy flights. 相似文献
14.
We investigate the dynamic event-triggered state estimation for uncertain complex networks with hybrid delays suffering from both deception attacks and denial-of-service attacks.Firstly,the effects of time-varying delays and finitedistributed delays are considered during data transmission between nodes.Secondly,a dynamic event-triggered scheme(ETS)is introduced to reduce the frequency of data transmission between sensors and estimators.Thirdly,by considering the discussed plant,dynamic ETS,state estimator,and hybrid attacks into a unified framework,this framework is transferred into a novel dynamical model.Furthermore,with the help of Lyapunov stability theory and linear matrix inequality techniques,sufficient condition to ensure that the system is exponentially stable and satisfies H∞performance constraints is obtained,and the design algorithm for estimator gains is given.Finally,two numerical examples verify the effectiveness of the proposed method. 相似文献
15.
Observations of radio signals from distant pulsars provide a valuable tool for investigation of interstellar turbulence. The time shapes of the signals are the result of pulse broadening by the fluctuating electron density in the interstellar medium. While the scaling of the shapes with the signal frequency is well understood, the observed anomalous scaling with respect to the pulsar distance has remained a puzzle for more than 30 years. We propose a new model for interstellar electron density fluctuations, which explains the observed scaling relations. We suggest that these fluctuations obey Lévy statistics rather than Gaussian statistics, as assumed in previous treatments of interstellar scintillations. 相似文献
16.
Based on the maximum entropy principle, we present a density matrix of mesoscopic RLC circuit to make it possible to analyze the connection of the initial condition with temperature. Our results show that the quantum state evolution is closely related to the initial condition, and that the system evolves to generalized coherent state if it is in ground state initially, and evolves to squeezed state if it is in excited state initially. 相似文献
19.
Lévy walk with multiple internal states can effectively model the motion of particles that don’t immediately move back to the directions or areas which they come from. When the Lévy walk behaves superdiffusion, it is discovered that the non-immediately-repeating property, characterized by the constructed transition matrix, has no influence on the particle’s mean square displacement (MSD) or Pearson coefficient. This is a kind of stable property of Lévy walk. However, if the Lévy walk shows the dynamical behaviors of normal diffusion, then the effect of non-immediately-repeating emerges. For the Lévy walk with some particular transition matrices, it may display nonsymmetric dynamics; in these cases, the behaviors of their variances are detailedly discussed, especially some comparisons with the ones of the continuous time random walks are made (a striking difference is the changes of the exponents of the variances). The first passage time distribution and its average of Lévy walks are simulated, the results of which turn out that the first passage time can distinguish Lévy walks with different transition matrices, while the MSD can not. 相似文献
20.
We consider a previously devised model describing Lévy random walks [I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E
79, 011110 (2009); I. Lubashevsky, R. Friedrich, A. Heuer, Phys. Rev. E 80, 031148
(2009)]. It is demonstrated numerically that the given model describes Lévy random walks with superdiffusive, ballistic, as
well as superballistic dynamics. Previously only the superdiffusive regime has been analyzed. In this model the walker velocity
is governed by a nonlinear Langevin equation. Analyzing the crossover from small to large time scales we find the time scales
on which the velocity correlations decay and the walker motion essentially exhibits Lévy statistics. Our analysis is based
on the analysis of the geometric means of walker displacements and allows us to tackle probability density functions with
power-law tails and, correspondingly, divergent moments. 相似文献
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