scholarly journals Investigating non-uniform scaling behaviour in temporal fluctuations of seismicity

2008 ◽  
Vol 8 (5) ◽  
pp. 973-976 ◽  
Author(s):  
L. Telesca ◽  
M. Lovallo
Keyword(s):  
Time Series ◽  
Power Law ◽  
Central Italy ◽  
Fluctuation Analysis ◽  
Temporal Fluctuations ◽  
Scaling Behaviour ◽  
Scaling Region ◽  
Detrended Fluctuation ◽  
Large Earthquakes ◽  
Uniform Scaling

Abstract. Scaling behaviour in nonstationary time series can be successfully detected using the detrended fluctuation analysis (DFA). Observational time series often do not show a stable and uniform scaling behaviour, given by the presence of a unique clear scaling region. The deviations from uniform power-law scaling, which suggest the presence of changing dynamics in the system under study, can be identified and quantified using an appropriate instability index. In this framework, the scaling behaviour of the 1981–2007 seismicity in Umbria-Marche (central Italy), which is one of the most seismically active areas in Italy, was investigated. Significant deviations from uniform power-law scaling in the seismic temporal fluctuations were revealed mostly linked with the occurrence of rather large earthquakes or seismic clusters.

scholarly journals MULTIFRACTAL ANALYSIS OF STRESS TIME SERIES DURING ULTRATHIN LUBRICANT FILM MELTING

2010 ◽  
Vol 09 (01) ◽  
pp. 19-35 ◽  
Author(s):  
ALEXEI V. KHOMENKO ◽  
IAKOV A. LYASHENKO ◽  
VADIM N. BORISYUK
Keyword(s):  
Time Series ◽  
Power Law ◽  
Lubricant Film ◽  
Fluctuation Analysis ◽  
Power Law Distribution ◽  
Stick Slip ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Flat Surfaces ◽  
Self Similar ◽  
Detrended Fluctuation

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of stick-slip friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.

scholarly journals DETRENDED FLUCTUATION ANALYSIS OF THE TCP-RED ALGORITHM

2009 ◽  
Vol 19 (12) ◽  
pp. 4237-4245 ◽  
Author(s):  
XI CHEN ◽  
SIU-CHUNG WONG ◽  
CHI K. TSE ◽  
LJILJANA TRAJKOVIĆ
Keyword(s):  
Time Series ◽  
Long Range ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Time Series Data ◽  
Analytical Models ◽  
Series Data ◽  
Fluctuation Analysis ◽  
Scaling Exponent ◽  
Detrended Fluctuation

It has been observed that Internet gateways employing Transport Control Protocol (TCP) and the Random Early Detection (RED) control algorithm may exhibit instability and oscillatory behavior. Most control methods proposed in the past have been based on analytical models that rely on statistical measurements of network parameters. In this paper, we apply the detrended fluctuation analysis (DFA) method to analyze stability of the TCP-RED system. The DFA is used to analyze time-series data and generate power-law scaling exponents, which indicate the long-range correlations of the time series. We quantify the stability of the TCP-RED system by examining the variation of the DFA power-law scaling exponent when the system parameters are varied. We also study the long-range power-law correlations of TCP window periods.

Scaling analysis of hyperchaotic time series

2017 ◽  
Vol 28 (07) ◽  
pp. 1750094 ◽  
Author(s):  
J. S. Murguía
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Dynamical Evolution ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Scaling Analysis ◽  
Detrended Fluctuation ◽  
Hyperchaotic Systems

The time series of the states of several well-known hyperchaotic systems are analyzed numerically using the detrended fluctuation analysis based on the discrete wavelet transform. We report the finding of significant scaling behaviors (power-law like) in some of these time series, which can be used as an additional characteristic distinguishing the dynamical evolution of such systems.

scholarly journals AUTOMATICALLY DETECTING "SIGNIFICANT EVENTS" ON SenseCam

2013 ◽  
Vol 11 (06) ◽  
pp. 1350050 ◽  
Author(s):  
NA LI ◽  
MARTIN CRANE ◽  
HEATHER J. RUSKIN
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Time Windows ◽  
Fluctuation Analysis ◽  
Discrete Wavelet ◽  
Dominant Eigenvalue ◽  
Multiple Time ◽  
Correlation Relationship ◽  
Significant Events ◽  
Detrended Fluctuation

SenseCam is an effective memory-aid device that can automatically record images and other data from the wearer's whole day. The main issue is that, while SenseCam produces a sizeable collection of images over the time period, the vast quantity of captured data contains a large percentage of routine events, which are of little interest to review. In this article, the aim is to detect "Significant Events" for the wearers. We use several time series analysis methods such as Detrended Fluctuation Analysis (DFA), Eigenvalue dynamics and Wavelet Correlations to analyse the multiple time series generated by the SenseCam. We show that Detrended Fluctuation Analysis exposes a strong long-range correlation relationship in SenseCam collections. Maximum Overlap Discrete Wavelet Transform (MODWT) was used to calculate equal-time Correlation Matrices over different time scales and then explore the granularity of the largest eigenvalue and changes of the ratio of the sub-dominant eigenvalue spectrum dynamics over sliding time windows. By examination of the eigenspectrum, we show that these approaches enable detection of major events in the time SenseCam recording, with MODWT also providing useful insight on details of major events. We suggest that some wavelet scales (e.g., 8 minutes–16 minutes) have the potential to identify distinct events or activities.

Power-Law Fluctuation in Expressway Traffic Flow: Detrended Fluctuation Analysis

2006 ◽  
Vol 75 (3) ◽  
pp. 034002 ◽  
Author(s):  
S. Tadaki ◽  
M. Kikuchi ◽  
A. Nakayama ◽  
K. Nishinari ◽  
A. Shibata ◽  
...  
Keyword(s):  
Traffic Flow ◽  
Power Law ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Detrended Fluctuation

scholarly journals Technical Note: Long-term memory effect in the atmospheric CO<sub>2</sub> concentration at Mauna Loa

2006 ◽  
Vol 6 (6) ◽  
pp. 11957-11970 ◽  
Author(s):  
C. Varotsos ◽  
M.-N. Assimakopoulos ◽  
M. Efstathiou
Keyword(s):  
Carbon Dioxide ◽  
Time Series ◽  
Power Law ◽  
Carbon Dioxide Concentration ◽  
Global Climate Models ◽  
Fluctuation Analysis ◽  
Original Time Series ◽  
Mauna Loa ◽  
Carbon Dioxide Concentrations ◽  
Original Time

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

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