scholarly journals On the Dimension of the Solar Activity Attractor

1993 ◽  
Vol 157 ◽  
pp. 91-95
Author(s):  
C.M. Orzaru
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Solar Activity ◽  
Correlation Dimension ◽  
Chaotic Behaviour ◽  
The Other ◽  
Short Series ◽  
Sunspot Numbers ◽  
First Case ◽  
Characteristic Measure

The correlation dimension D(2) as a characteristic measure of the regular or chaotic behaviour of the solar dynamical system has been calculated. The algorithm suggested by Grassberger and Procaccia (1983) has been applied to time series of relative sunspot numbers and of areas of sunspots and faculae. In the first case, a correlation dimension D(2) ≃ 1.5 has been found; in the other two cases, the algorithm was not convergent, the results obtained being not relevant, due to the too short series of data available.

Planetary Modulation of Solar Activity

1967 ◽  
Vol 1 (2) ◽  
pp. 53-54 ◽  
Author(s):  
E. K. Bigg ◽  
P. S. Mulhall
Keyword(s):  
Solar Activity ◽  
Solar Surface ◽  
Relative Equilibrium ◽  
High Tide ◽  
The Other ◽  
The Sun ◽  
Sunspot Numbers ◽  
Tidal Forces ◽  
Wide Range ◽  
Degree Of Control

It has recently been shown that the planet Mercury exerts a small control on relative sunspot numbers, the degree of control depending on the positions of the other planets.This paper describes the results of extending the work to include all the planets.As a working hypothesis we have assumed that gravitational tidal forces induced on the Sun by the planets may modulate solar activity and have accordingly calculated relative equilibrium ‘high tide’ displacements of the solar surface for each day from the positions, masses and distances of the first six planets. Although the tides are very slight, the mass of displaced material is appreciable and varies over the very wide range of nearly 5 to 1.

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.

scholarly journals A comparative study on chaoticity of equatorial/low latitude ionosphere over Indian subcontinent during geomagnetically quiet and disturbed periods

2010 ◽  
Vol 17 (6) ◽  
pp. 765-776 ◽  
Author(s):  
K. Unnikrishnan
Keyword(s):  
Time Series ◽  
Prediction Error ◽  
Correlation Dimension ◽  
Linear Prediction ◽  
Indian Subcontinent ◽  
Surrogate Data ◽  
Chaotic Behaviour ◽  
Quiet Period ◽  
Nonlinear Prediction ◽  
Non Linear

Abstract. In the present study, the latitudinal aspect of chaotic behaviour of ionosphere during quiet and storm periods are analyzed and compared by using GPS TEC time series measured at equatorial trough, crest and outside crest stations over Indian subcontinent, by employing the chaotic quantifiers like Lyapunov exponent (LE), correlation dimension (CD), entropy and nonlinear prediction error (NPE). It is observed that the values of LE are low for storm periods compared to those of quiet periods for all the stations considered here. The lowest value of LE is observed at the trough station, Agatti (2.38° N, Geomagnetically), and highest at crest station, Mumbai (10.09° N, Geomagnetically) for both quiet and storm periods. The values of correlation dimension computed for TEC time series are in the range 2.23–2.74 for quiet period, which indicate that equatorial ionosphere may be described with three variables during quiet period. But the crest station Mumbai shows a higher value of CD (3.373) during storm time, which asserts that four variables are necessary to describe the system during storm period. The values of non linear prediction error (NPE) are lower for Agatti (2.38° N, Geomagnetically) and Jodhpur (18.3° N, Geomagnetically), during storm period, compared to those of quiet period, mainly because of the predominance of non linear aspects during storm periods The surrogate data test is carried out and on the basis of the significance of difference of the original data and surrogates for various aspects, the surrogate data test rejects the null hypothesis that the time series of TEC during storm and quiet times represent a linear stochastic process. It is also observed that using state space model, detrended TEC can be predicted, which reasonably reproduces the observed data. Based on the values of the above quantifiers, the features of chaotic behaviour of equatorial trough crest and outside the crest regions of ionosphere during geomagnetically quiet and disturbed periods are briefly discussed.

Influences of the solar activity on the correlation dimension of underground muon time series at 34 MWE

1999 ◽  
Vol 23 (3) ◽  
pp. 595-598
Author(s):  
S Yasue ◽  
K Munakata ◽  
T Shiozawa ◽  
A Ogi ◽  
K Kudela
Keyword(s):  
Time Series ◽  
Solar Activity ◽  
Correlation Dimension ◽  
Underground Muon

Producers' Response to Changes in Prices and Marketing Policies: A Case Study of Sugarcane and Paddy in Eastern U.P. by S. C. Gupta and A. Majid. New York: Asia Publishing House, 1965.

1968 ◽  
Vol 8 (2) ◽  
pp. 308-309
Author(s):  
Mohammad Irshad Khan
Keyword(s):  
New York ◽  
Time Series ◽  
Time Series Data ◽  
Publishing House ◽  
Economic Incentives ◽  
The Other ◽  
Series Data ◽  
Poor Countries ◽  
Northern India

It is alleged that the agricultural output in poor countries responds very little to movements in prices and costs because of subsistence-oriented produc¬tion and self-produced inputs. The work of Gupta and Majid is concerned with the empirical verification of the responsiveness of farmers to prices and marketing policies in a backward region. The authors' analysis of the respon¬siveness of farmers to economic incentives is based on two sets of data (concern¬ing sugarcane, cash crop, and paddy, subsistence crop) collected from the district of Deoria in Eastern U.P. (Utter Pradesh) a chronically foodgrain deficit region in northern India. In one set, they have aggregate time-series data at district level and, in the other, they have obtained data from a survey of five villages selected from 170 villages around Padrauna town in Deoria.

A NEW APPROACH TO THE STUDY OF COORDINATIVE CONSTRUCTIONS

2019 ◽  
pp. 175-187
Author(s):  
Anna Varnayeva
Keyword(s):  
Characteristic Property ◽  
Mathematical Concept ◽  
The Other ◽  
New Approach ◽  
Logical Aspect ◽  
First Case

Coordinative constructions are traditionally opposed to subordinative constructions. However, this opposition comes down to denial of dependence in coordinative constructions. Thereby the parity of these two constructions does not come to light: subordinative construction can be described without coordinative one. This situation is not improved by detection of a coordinative triangle in all coordinative constructions. The article shows a new approach in the study of coordinative constructions: a coordinative construction is a system; there are not only specific relations – a coordinative triangle, – but also specific elements. Novelty of the study consists in the address to extralinguistic facts, viz. a mathematical concept of a set and its elements. There are a lot of similarities between them. A set in mathematics includes generalizing elements and the composed row in coordinative constructions; in the first case the set is not partitioned, in the second case it is partitioned. In mathematics equivalent components in coordinative constructions correspond to the set elements. A characteristic property in mathematics is homogeneity in coordinative constructions and etc. It is firstly demonstrated, that coordinative and subordinative constructions are correlative and the study of one construction is impossible without the study of the other one. Their parity is shown in coordinative constructions with elements of one set, in subordinative ones with elements of different sets. Cf.: roses and tulips –red roses. In the coordinatiму construction elements of one set are called: «flowers »; in the subordinative construction there are elements of different sets: «flowers » and «colors». It should be noted that the mathematical concept of a set relates to so called logical aspect in linguistics or thinking about reality.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

scholarly journals The Connections between COVID-19 and the Energy Commodities Prices: Evidence through the Dynamic Time Warping Method

Energies ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 4024
Author(s):  
Krzysztof Dmytrów ◽  
Joanna Landmesser ◽  
Beata Bieszk-Stolorz
Keyword(s):  
Time Series ◽  
Palm Oil ◽  
Dynamic Time Warping ◽  
Global Economy ◽  
Price Change ◽  
Commodity Prices ◽  
The Other ◽  
Time Warping ◽  
Heating Oil ◽  
Dynamic Time

The main objective of the study is to assess the similarity between the time series of energy commodity prices and the time series of daily COVID-19 cases. The COVID-19 pandemic affects all aspects of the global economy. Although this impact is multifaceted, we assess the connections between the number of COVID-19 cases and the energy commodities sector. We analyse these connections by using the Dynamic Time Warping (DTW) method. On this basis, we calculate the similarity measure—the DTW distance between the time series—and use it to group the energy commodities according to their price change. Our analysis also includes finding the time shifts between daily COVID-19 cases and commodity prices in subperiods according to the chronology of the COVID-19 pandemic. Our findings are that commodities such as ULSD, heating oil, crude oil, and gasoline are weakly associated with COVID-19. On the other hand, natural gas, palm oil, CO2 allowances, and ethanol are strongly associated with the development of the pandemic.

scholarly journals Historical sunspot records

2020 ◽  
Vol 17 (1) ◽  
Author(s):  
Rainer Arlt ◽  
José M. Vaquero
Keyword(s):  
Time Series ◽  
19Th Century ◽  
Sunspot Number ◽  
Final Part ◽  
Group Sunspot ◽  
Naked Eye ◽  
Sunspot Numbers ◽  
The 19Th Century ◽  
Physical Quantities

AbstractSunspot observations are available in fairly good numbers since 1610, after the invention of the telescope. This review is concerned with those sunspot observations of which longer records and drawings in particular are available. Those records bear information beyond the classical sunspot numbers or group sunspot numbers. We begin with a brief summary on naked-eye sunspot observations, in particular those with drawings. They are followed by the records of drawings from 1610 to about 1900. The review is not a compilation of all known historical sunspot information. Some records contributing substantially to the sunspot number time series may therefore be absent. We also glance at the evolution of the understanding of what sunspots actually are, from 1610 to the 19th century. The final part of the review illuminates the physical quantities that can be derived from historical drawings.

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