Strange Attractor in Nonlinear Fluctuations of Length Of the Day (LOD) Time Series

2013 ◽  
pp. 61-67 ◽  
Author(s):  
R.K. Tiwari ◽  
J.G. Negi ◽  
K.N.N. Rao
Keyword(s):  
Time Series ◽  
Strange Attractor ◽  
Length Of The Day ◽  
Nonlinear Fluctuations

scholarly journals Evidence for nonlinear and chaotic behaviour in pulsar spin-down rates

2012 ◽  
Vol 8 (S291) ◽  
pp. 495-495
Author(s):  
Andrew Seymour ◽  
Duncan Lorimer
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Nonlinear Equations ◽  
Strange Attractor ◽  
Correlation Dimension ◽  
Chaotic Dynamics ◽  
Structural Information ◽  
Chaotic Behaviour ◽  
Present Evidence

AbstractWe present evidence for chaotic dynamics in pulsar spin-down rates originally measured by Lyne et al. (2010). Using techniques that allow us to re-sample the original measurements without losing structural information, we have searched for evidence for a strange attractor in the time series of frequency derivative for each pulsar. Our measurements of correlation dimension and Lyapunov exponent show, particularly in the case of PSR B1828-11, that the underlying behavior appears to be driven by a strange attractor with approximately three governing nonlinear equations.

Non-Linear Properties of the VIX Index

2017 ◽  
Vol 5 (2) ◽  
pp. 16-24
Author(s):  
L. Magafas ◽  
M. Hanias ◽  
A. Tavlatou ◽  
P. Kostantaki
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Strange Attractor ◽  
Series Analysis ◽  
The World ◽  
Non Linear ◽  
The Future ◽  
Stock Indexes

This paper applies non-linear methods to analyze and predict the daily VIX index which is one of the most important stock indexes in the world. The aim of the analysis is to quantitatively show if the corresponding time series is a deterministic chaotic one and if one or more days ahead prediction can be achieved. The research employs Grassberger and Procaccia's methodology in the time series analysis in order to estimate the correlation and minimum embedding dimensions of the corresponding strange attractor. To achieve from the sample a multistep ahead prediction, the article gives the average for overall neighbours' projections of k-steps into the future. These results make the present work a valuable tool for traders, investors, and funds.

scholarly journals Method of attractor reconstruction in modeling the integral risk indicator

2021 ◽  
Vol 2094 (3) ◽  
pp. 032010
Author(s):  
L M Bogdanova ◽  
S Ya Nagibin ◽  
O A Rabinovich
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
Strange Attractor ◽  
Real Data ◽  
Industrial Safety ◽  
Risk Indicator ◽  
Safety Risk ◽  
Attractor Reconstruction

Abstract This study examines a mathematical model for forecasting the dynamics of changes in the industrial safety risk indicator of an enterprise. The results of the development of a method for reconstructing the attractor of the integral risk indicator based on the Grassberger-Prokacchia algorithm, which is currently the most popular for analyzing time series and allowing automating the process of calculating a parameter that determines the number of points, for making a forecast. There are results of estimating the forecast of the dynamics of the behavior for a strange attractor, obtained on the basis of real data.

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

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