共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Although the multifractal singularity spectrum revealed the distribution of singularity exponent, it failed to consider the temporal information, therefore it is hard to describe the dynamic evolving process of non-stationary and nonlinear systems. In this paper, we aim for a multifractal analysis and propose a time-singularity multifractal spectrum distribution (TS-MFSD), which will hopefully reveal the spatial dynamic character of fractal systems. Similar to the Wigner–Ville time-frequency distribution, the time-delayed conjugation of fractal signals is selected as the windows function. Furthermore, the time-varying Holder exponent and the time-varying wavelet singularity exponent are deduced based on the instantaneous self-correlation fractal signal. The time-singularity exponent distribution i.e. TS-MFSD is proposed, which involves time-varying Hausdorff singularity spectrum distribution, time-varying large deviation multifractal spectrum and time-varying Legendre spectrum distribution, which exhibit the singularity exponent distribution of fractal signal at arbitrary time. Finally, we studied the algorithm of the TS-MFSD based on the wavelet transform module maxima method, analyzed and discussed the characteristic of TS-MFSD based on Devil Staircase signal, stochastic fractional motion and real sea clutter. 相似文献
3.
Maricel Agop Stefan Andrei Irimiciuc Adrian Ghenadi Luminita Bibire Stefan Toma Tudor-Cristian Petrescu Dorin Vaideanu Cristina Marcela Rusu Alina Gavrilut Decebal Vasincu 《Entropy (Basel, Switzerland)》2021,23(2)
In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”. 相似文献
4.
海杂波的奇异谱分析不仅能从理论上揭示海洋表面的动力学机理,同时也是对海探测雷达的关键技术之一.本文提出基于小波leaders的海杂波时变奇异谱分析方法,将时间信息引入海杂波的奇异谱分析之中,从而实现动态的解析描述海杂波随时间变化的奇异谱特性.在理论上,通过信号自身加窗,将时间信息引入传统的奇异谱(或称多重分形谱),实现了对海杂波时变奇异谱分布分析;在算法上,充分利用了小波leaders技术对于多种奇异性的提取能力(包括chirp奇异性和cusp奇异性),通过对时变奇异性指数和时变尺度函数的Legendre变换,实现对海杂波时变奇异谱分布的计算;在应用部分,采用经典的多重分形模型——随机小波序列(RWC)以及三级海态条件下连续波多普勒体制雷达海杂波进行仿真分析,实验结果表明:1)基于小波leaders的奇异谱分布能跟踪海杂波的时变尺度特性,有效展示其时变奇异性谱分布;2)算法具有较好的负矩特性和统计收敛性.该方法能为复杂非线性系统及随机多重分形信号分析提供参考. 相似文献
5.
6.
Over the last twenty years, many studies have been made of radiative transfer in scaling cloud fields, the vast majority of which have been limited to numerical studies in clouds with relatively small optical thickness. An exception to this was the development of a formalism for treating single scattering in optically thick but conservative multifractal clouds without significant holes. In part I of this paper we show how these results can be extended to general “universal” multifractal clouds dominated by low density “Lévy holes”. In part II, we demonstrate how the analytic single scattering results can be generalized to multiple scattering including the case of very thick clouds as well as to realistic nonconservative clouds. 相似文献
7.
8.
Chaos game representation (CGR) is proposed as a
scale-independent representation for DNA sequences and provides
information about the statistical distribution of oligonucleotides
in a DNA sequence. CGR images of DNA sequences represent some kinds of
fractal patterns, but the common multifractal analysis based on the
box counting method cannot deal with CGR images perfectly. Here, the
wavelet transform modulus maxima (WTMM) method is applied to the
multifractal analysis of CGR images. The results show that the
scale-invariance range of CGR edge images can be extended to three
orders of magnitude, and complete singularity spectra can be
calculated. Spectrum parameters such as the singularity spectrum
span are extracted to describe the statistical character of DNA
sequences. Compared with the singularity spectrum span, exon
sequences with a minimal spectrum span have the most uniform
fractal structure. Also, the singularity spectrum parameters are
related to oligonucleotide length, sequence component and species,
thereby providing a method of studying the length polymorphism of
repeat oligonucleotides. 相似文献
9.
Yong-Hai Zhang Bao-Feng BaiJian-Qiang Li Jing-Bo ChenChang-Yu Shen 《Applied Surface Science》2011,257(7):2984-2989
In the present work, the building panel of glass fiber reinforced polyvinylidene chloride composite was prepared and the tensile fracture surfaces of the composites were investigated by the box-counting method of multifractal theory. It suggested that the tensile fracture surface of polyvinylidene chloride/glass fiber (PVDC/GF) composite exhibits multifractal features and the tensile fracture surface morphology of the composite have a strong dependence on the mechanical properties. The results showed that the variation of glass fiber content would lead to the change of mechanical properties, which were responsible for the tensile fracture morphology of PVDC/GF composite. Consequently, the gray value distribution characterizing the surface morphology on the tensile fracture surface would become more non-uniform or less due to this change. The multifractal spectrum could correspondingly mirror this variation according to multifractal methodology. It indicated that the width in multifractal spectrum is sensitive to the morphology of the tensile fractured surface. It is concluded that the multifractal spectrum is the result of the change in mechanical properties of the composites. Additionally, it also suggested that the tensile fracture of the composite is the result of the competition between ductile fracture and brittle fracture by comparing the multifractal spectra and the multifractal spectra would correspondingly change due to this competition. The more the percentage of ductile fracture is, the more rough the fracture surface, the larger the width in the multifractal spectrum. Therefore, it is thought that the multifractal spectrum could feature the rough morphology of the tensile fractured surface and the mechanical properties quantitatively. 相似文献
10.
We introduce the notion of topological pressure for suspension flows over countable Markov shifts, and we develop the associated thermodynamic formalism. In particular, we establish a variational principle for the topological pressure, and an approximation property in terms of the pressure on compact invariant sets. As an application we present a multifractal analysis for the entropy spectrum of Birkhoff averages for suspension flows over countable Markov shifts. The domain of the spectrum may be unbounded and the spectrum may not be analytic. We provide explicit examples where this happens. We also discuss the existence of full measures on the level sets of the multifractal decomposition. 相似文献
11.
Ivanov PC Nunes Amaral LA Goldberger AL Havlin S Rosenblum MG Stanley HE Struzik ZR 《Chaos (Woodbury, N.Y.)》2001,11(3):641-652
We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics. 相似文献
12.
This paper reviews a class of multifractal models obtained via products of exponential Ornstein–Uhlenbeck processes driven by Lévy motion. Given a self-decomposable distribution, conditions for constructing multifractal scenarios and general formulas for their Renyi functions are provided. Together with several examples, a model with multifractal activity time is discussed and an application to exchange data is presented. 相似文献
13.
14.
W. Jeżewski 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,19(1):133-138
Scaling properties of the Gibbs distribution of a finite-size one-dimensional Ising model are investigated as the thermodynamic
limit is approached. It is shown that, for each nonzero temperature, coarse-grained probabilities of the appearance of particular
energy levels display multiscaling with the scaling length ℓ = 1/M
n, where n denotes the number of spins and Mn is the total number of energy levels. Using the multifractal formalism, the probabilities are argued to reveal also multifractal
properties.
Received 10 July 2000 and Received in final form 6 November 2000 相似文献
15.
提出了一种研究混响室问题的理论分析方法,从理想混响室的离散概率模型出发,采用蒙特卡罗模拟来获得室内电磁场量及其相关物理量的概率统计特性。运用该方法获得了混响室内若干场量(均为归一化值)的概率密度函数、室内一段均匀无耗单导体传输线的负载平均耦合截面及负载电流响应模值的概率分布,所得结果与已有文献给出的结果(包括由解析公式计算或测量所得的结果)吻合良好。由于蒙特卡罗方法的普适性,采用该方法可以获得任意待分析参量的全部概率统计特性(只要样本数足够大)。同时该方法无需针对具体混响室进行,只要在其测试区域能较好地与理想混响室的基本概率模型相吻合,就能给出较精确的计算结果,且其计算量远远小于基于全波分析的蒙特卡罗方法。 相似文献
16.
A. Bershadskii 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(2):141-142
It is shown that quasi Bernoulli fluctuations, which appear at a morphological phase transition, can be considered as a statistical
basis for multifractal processes with constant multifractal specific heat in a wide class of random and disordered systems.
This class contains at least following processes: percolation, diffusion-limited aggregation and corrosion, Lorenz like attractors,
and mesoscopic systems with Anderson transition.
Received: 14 April 1998 / Revised and Accepted: 20 April 1998 相似文献
17.
The singularity exponent (SE) is the characteristic parameter of fractal and multifractal signals. Based on SE, the fractal dimension reflecting the global self-similar character, the instantaneous SE reflecting the local self-similar character, the multifractal spectrum (MFS) reflecting the distribution of SE, and the time-varying MFS reflecting pointwise multifractal spectrum were proposed. However, all the studies were based on the depiction of spatial or differentiability characters of fractal signals. Taking the SE as the independent dimension, this paper investigates the fractal energy measurement (FEM) and the singularity energy spectrum (SES) theory. Firstly, we study the energy measurement and the energy spectrum of a fractal signal in the singularity domain, propose the conception of FEM and SES of multifractal signals, and investigate the Hausdorff measure and the local direction angle of the fractal energy element. Then, we prove the compatibility between FEM and traditional energy, and point out that SES can be measured in the fractal space. Finally, we study the algorithm of SES under the condition of a continuous signal and a discrete signal, and give the approximation algorithm of the latter, and the estimations of FEM and SES of the Gaussian white noise, Fractal Brownian motion and the multifractal Brownian motion show the theoretical significance and application value of FEM and SES. 相似文献
18.
In this article, we investigated the multifractality and its underlying formation mechanisms in international crude oil markets, namely, Brent and WTI, which are the most important oil pricing benchmarks globally. We attempt to find the answers to the following questions: (1) Are those different markets multifractal? (2) What are the dynamical causes for multifractality in those markets (if any)? To answer these questions, we applied both multifractal detrended fluctuation analysis (MF-DFA) and multifractal singular spectrum analysis (MF-SSA) based on the partition function, two widely used multifractality detecting methods. We found that both markets exhibit multifractal properties by means of these methods. Furthermore, in order to identify the underlying formation mechanisms of multifractal features, we destroyed the underlying nonlinear temporal correlation by shuffling the original time series; thus, we identified that the causes of the multifractality are influenced mainly by a nonlinear temporal correlation mechanism instead of a non-Gaussian distribution. At last, by tracking the evolution of left- and right-half multifractal spectra, we found that the dynamics of the large price fluctuations is significantly different from that of the small ones. Our main contribution is that we not only provided empirical evidence of the existence of multifractality in the markets, but also the sources of multifractality and plausible explanations to current literature; furthermore, we investigated the different dynamical price behaviors influenced by large and small price fluctuations. 相似文献
19.
We show that the fractal growth described by the dielectric breakdown model exhibits a phase transition in the multifractal spectrum of the growth measure. The transition takes place because the tip splitting of branches forms a fixed angle. This angle is eta dependent but it can be rescaled onto an "effectively" universal angle of the diffusion-limited aggregation branching process. We derive an analytic rescaling relation which is in agreement with numerical simulations. The dimension of the clusters decreases linearly with the angle and the growth becomes non-ractal at an angle close to 74 degrees (which corresponds to eta = 4.0+/-0.3). 相似文献
20.
We investigate the multifractal properties of price increments in the cases of derivative and spot markets. Through the multifractal detrended fluctuation analysis, we estimate the generalized Hurst and the Renyi exponents for price fluctuations. By deriving the singularity spectrum from the above exponents, we quantify the multifractality of a financial time series and compare the multifractal properties of two different markets. The different behavior of each agent-group in transactions is also discussed. In order to identify the nature of the underlying multifractality, we apply the method of surrogate data to both sets of financial data. It is shown that multifractality due to a fat-tailed distribution is significant. 相似文献