Multiscale measures of phase-space trajectories

2020 ◽  
Author(s):  
Tommaso Alberti ◽  
Giuseppe Consolini ◽  
Peter D. Ditlevsen ◽  
Reik V. Donner ◽  
Virgilio Quattrociocchi
Keyword(s):  
Phase Space ◽  
Function Analysis ◽  
Fractal Dimensions ◽  
Intrinsic Mode Functions ◽  
Electromagnetic Environment ◽  
Space Trajectories ◽  
Mode Decomposition ◽  
The Lorenz System ◽  
Generalized Dimensions ◽  
Phase Space Trajectories

<p>Several attempts have been made in characterizing the multiscale nature of fluctuations from nonlinear and nonstationary time series. Particularly, the study of their fractal structure has made use of different approaches like the structure function analysis, the evaluation of the generalized dimensions, and so on. Here we report on a different approach for characterizing phase-space trajectories by using the empirical modes derived via the Empirical Mode Decomposition (EMD) method. We show how the derived Intrinsic Mode Functions (IMFs) can be used as source of local (in terms of scales) information allowing us in deriving multiscale measures when looking at the behavior of the generalized fractal dimensions at different scales. This formalism is applied to three pedagogical examples like the Lorenz system, the Henon map, and the standard map. We also show that this formalism is readily applicable to characterize both the behavior of the Earth’s climate during the past 5 Ma and the dynamical properties of the near-Earth electromagnetic environment as monitored by the SYM-H index.</p>

scholarly journals Quantum revival patterns from classical phase-space trajectories

2019 ◽  
Vol 99 (4) ◽  
Author(s):  
Gabriel M. Lando ◽  
Raúl O. Vallejos ◽  
Gert-Ludwig Ingold ◽  
Alfredo M. Ozorio de Almeida
Keyword(s):  
Phase Space ◽  
Space Trajectories ◽  
Quantum Revival ◽  
Classical Phase Space ◽  
Phase Space Trajectories

scholarly journals Nonlinear multivariable analysis of SOI and local precipitation and temperature

2005 ◽  
Vol 12 (1) ◽  
pp. 67-74 ◽  
Author(s):  
Y.-H. Jin ◽  
A. Kawamura ◽  
K. Jinno ◽  
R. Berndtsson
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Southern Oscillation ◽  
Statistical Prediction ◽  
Meteorological Variables ◽  
Space Trajectories ◽  
Local Climate ◽  
Prediction Techniques ◽  
Precipitation And Temperature ◽  
Phase Space Trajectories

Abstract. Global climate variability affects important local hydro-meteorological variables like precipitation and temperature. The Southern Oscillation (SO) is an easily quantifiable major driving force that gives impact on regional and local climate. The relationships between SO and local climate variation are, however, characterized by strongly nonlinear processes. Due to this, teleconnections between global-scale hydro-meteorological variables and local climate are not well understood. In this paper, we suggest to study these processes in terms of nonlinear dynamics. Consequently, the nonlinear dynamic relationship between the Southern Oscillation Index (SOI), precipitation, and temperature in Fukuoka, Japan, is investigated using a nonlinear multivariable approach. This approach is based on the joint variation of these variables in the phase space. The joint phase-space variation of SOI, precipitation, and temperature is studied with the primary objective to obtain a better understanding of the dynamical evolution of local hydro-meteorological variables affected by global atmospheric-oceanic phenomena. The results from the analyses display rather clear low-order phase space trajectories when treating the time series individually. However, when plotting phase space trajectories for several time series jointly, complicated higher-order nonlinear relationships emerge between the variables. Consequently, simple data-driven prediction techniques utilizing phase-space characteristics of individual time series may prove successful. On the other hand, since either the time series are too short and/or the phase-space properties are too complex when analysing several variables jointly, it may be difficult to use multivariable statistical prediction techniques for the present investigated variables. In any case, it is essential to further pursue studies regarding links between the SOI and observed local climatic and other geophysical variables even if these links are not fully understood in physical terms.

Invariant Manifold Detection From Phase Space Trajectories

2008 ◽  
Author(s):  
Joseph Kuehl ◽  
David Chelidze
Keyword(s):  
Phase Space ◽  
Invariant Manifold ◽  
Invariant Manifolds ◽  
Basins Of Attraction ◽  
Detection Methods ◽  
Trajectory Data ◽  
Space Trajectories ◽  
Data Set ◽  
Phase Space Warping ◽  
Phase Space Trajectories

Invariant manifolds provide important information about the structure of flows. When basins of attraction are present, the stable invariant manifold serves as the boundary between these basins. Thus, in experimental applications such as vibrations problems, knowledge of these manifolds is essential to understanding the evolution of phase space trajectories. Most existing methods for identifying invariant manifolds of a flow rely on knowledge of the flow field. However, in experimental applications only knowledge of phase space trajectories is available. We provide modifications to several existing invariant manifold detection methods which enables them to deal with trajectory only data, as well as introduce a new method based on the concept of phase space warping. The method of Stochastic Interrogation applied to the damped, driven Duffing equation is used to generate our data set. The result is a set of trajectory data which randomly populates a phase space. Manifolds are detected from this data set using several different methods. First is a variation on manifold “growing,” and is based on distance of closest approach to a hyperbolic trajectory with “saddle like behavior.” Second, three stretching based schemes are considered. One considers the divergence of trajectory pairs, another quantifies the deformation of a nearest neighbor cloud, and the last uses flow fields calculated from the trajectory data. Finally, the new phase space warping method is introduced. This method takes advantage of the shifting (warping) experienced by a phase space as the parameters of the system are slightly varied. This results in a shift of the invariant manifolds. The region spanned by this shift, provides a means to identify the invariant manifolds. Results show that this method gives superior detection and is robust with respect to the amount of data.

EMD fractal feature extraction technique in fingerprint of medicinal herbs

2015 ◽  
Vol 13 (04) ◽  
pp. 1550022
Author(s):  
Jianwei Du ◽  
Zhengguang Xu ◽  
Zhichun Mu ◽  
Yuan Yan Tang ◽  
Limin Cui ◽  
...  
Keyword(s):  
Recognition Rate ◽  
Low Frequency ◽  
Fractal Dimensions ◽  
Medicinal Herbs ◽  
The Novel ◽  
Intrinsic Mode Functions ◽  
Special Situation ◽  
Novel Approach ◽  
Mode Decomposition ◽  
Wavelet Features

This paper proposes the fractal features for glycyrrhiza fingerprint of medicinal herbs, to obtain the intrinsic mode functions (IMFs) from high to low frequency by using empirical mode decomposition (EMD). The EMD fractal features are extracted through computing the fractal dimensions of each IMF. The novel approach is applied to the recognition of the three types of glycyrrhiza fingerprints. Experiments show that EMD fractal features have better recognition rate than that of the traditional ones in the case of concentration-change, i.e. the number of peak and peak drift of sample which has slight changes. An existing method to extract the fractal features for fingerprint of medicinal herbs based on wavelet transform, which is called fractal-wavelet features, was presented. This method has anti-jamming property against the change of samples concentration. However, the recognition rate based on fractal-wavelet features is not satisfactory when fingerprint of medicinal herbs has some slight concentrations changes, the number of peak and peak drift of samples are processed in the special situation.

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