BISTABLE BEHAVIOR OF A KERR LENS MODE LOCKED Ti:SAPPHIRE LASER

2008 ◽  
Vol 18 (06) ◽  
pp. 1719-1726 ◽  
Author(s):  
MARCELO G. KOVALSKY ◽  
ALEJANDRO A. HNILO
Keyword(s):  
Numerical Simulation ◽  
Time Series ◽  
Deterministic Chaos ◽  
Embedding Dimension ◽  
Bistable Behavior ◽  
Ti:Sapphire Laser ◽  
Simulation Based ◽  
Iterative Maps ◽  
Low Dimensional ◽  
Structurally Stable

Kerr lens mode locked Ti :Sapphire lasers can operate in at least two pulsed modes. Several models were developed with the aim to describe the characteristics of these modes. Those based on iterative maps, can reproduce the structurally stable properties of each mode but are unable to describe the interaction between modes. In this paper, we present a numerical simulation based on a complete map equation that makes possible to accurately describe the bistability experimentally observed in the laser. With the numerical time series we determine that the bistable behavior corresponds to low dimensional deterministic chaos and calculate that the embedding dimension of the attractor is three.

scholarly journals Nonlinear time series analysis of geomagnetic pulsations

1994 ◽  
Vol 1 (2/3) ◽  
pp. 145-155 ◽  
Author(s):  
Z. Vörös ◽  
J. Verö ◽  
J. Kristek
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Correlation Dimension ◽  
Deterministic Chaos ◽  
Nonlinear Time Series ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Geomagnetic Pulsations ◽  
Series Analysis ◽  
Low Dimensional

Abstract. A detailed nonlinear time series analysis has been made of two daytime geomagnetic pulsation events being recorded at L'Aquila (Italy, L ≈ 1.6) and Niemegk (Germany, L ≈ 2.3). Grassberger and Procaccia algorithm has been used to investigate the dimensionality of physical processes. Surrogate data test and self affinity (fractal) test have been used to exclude coloured noise with power law spectra. Largest Lyapunow exponents have been estimated using the methods of Wolf et al. The problems of embedding, stability of estimations, spurious correlations and nonlinear noise reduction have also been discussed. The main conclusions of this work, which include some new results on the geomagnetic pulsations, are (1) that the April 26, 1991 event, represented by two observatory time series LAQ1 and NGK1 is probably due to incoherent waves; no finite correlation dimension was found in this case, and (2) that the June 18, 1991 event represented by observatory time series LAQ2 and NGK2, is due to low dimensional nonlinear dynamics, which include deterministic chaos with correlation dimension D2(NGK2) = 2.25 ± 0.05 and D2(NDK2) = 2.02 ± 0.03, and with positive Lyapunov exponents λmax (LAQ2) = 0.055 ± 0.003 bits/s and λmax (NGK2) = 0.052 ± 0.003 bits/s; the predictability time in both cases is ≈ 13 s.

scholarly journals CHAOS AND MUSIC: FROM TIME SERIES ANALYSIS TO EVOLUTIONARY COMPOSITION

2013 ◽  
Vol 23 (11) ◽  
pp. 1350181 ◽  
Author(s):  
MAXIMOS A. KALIAKATSOS-PAPAKOSTAS ◽  
MICHAEL G. EPITROPAKIS ◽  
ANDREAS FLOROS ◽  
MICHAEL N. VRAHATIS
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Analysis ◽  
Music Composition ◽  
Deterministic Chaos ◽  
Discrete Dynamical Systems ◽  
Main Motivation ◽  
Dynamical Characteristics ◽  
Series Analysis ◽  
Iterative Maps

Music is an amalgam of logic and emotion, order and dissonance, along with many combinations of contradicting notions which allude to deterministic chaos. Therefore, it comes as no surprise that several research works have examined the utilization of dynamical systems for symbolic music composition. The main motivation of the paper at hand is the analysis of the tonal composition potentialities of several discrete dynamical systems, in comparison to genuine human compositions. Therefore, a set of human musical compositions is utilized to provide "compositional guidelines" to several dynamical systems, the parameters of which are properly adjusted through evolutionary computation. This procedure exposes the extent to which a system is capable of composing tonal sequences that resemble human composition. In parallel, a time series analysis on the genuine compositions is performed, which firstly provides an overview of their dynamical characteristics and secondly, allows a comparative analysis with the dynamics of the artificial compositions. The results expose the tonal composition capabilities of the examined iterative maps, providing specific references to the tonal characteristics that they can capture.

NONLINEAR TIME-SERIES ANALYSIS OF THE GREEK EXCHANGE-RATE MARKET

2000 ◽  
Vol 10 (07) ◽  
pp. 1729-1758 ◽  
Author(s):  
A. S. ANDREOU ◽  
G. PAVLIDES ◽  
A. KARYTINOS
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Degrees Of Freedom ◽  
Nonlinear Dynamical Systems ◽  
Deterministic Chaos ◽  
Data Series ◽  
Nonlinear Dynamical ◽  
Series Analysis ◽  
Low Dimensional ◽  
Bds Test

Using concepts from the theory of chaos and nonlinear dynamical systems, a time-series analysis is performed on four major currencies against the Greek Drachma. The R/S analysis provided evidence for fractality due to noisy chaos in only two of the data series, while the BDS test showed that all four systems exhibit nonlinearity. Correlation dimension and related tests, as well as Lyapunov exponents, gave consistent results, which did not rule out the possibility of deterministic chaos for the two possibly fractal series, rejecting though the occurrence of a simple low-dimensional attractor, while the other two series seemed to have followed a behavior close to that of a random signal. SVD analysis, used to filter away noise, strongly supported the above findings and provided reliable evidence for the existence of an underlying system with a limited number of degrees-of-freedom only for those series found to exhibit fractality, while it revealed a noise domination over the remaining two. These results were further confirmed through a forecasting attempt using artificial neural networks.

DISTINGUISHING BETWEEN CHAOTIC AND STOCHASTIC SYSTEMS IN FINANCIAL TIME SERIES

2002 ◽  
Vol 13 (01) ◽  
pp. 31-39 ◽  
Author(s):  
MASSIMILIANO MENNA ◽  
GIULIA ROTUNDO ◽  
BRUNELLO TIROZZI
Keyword(s):  
Time Series ◽  
Correlation Dimension ◽  
Stochastic Systems ◽  
Financial Time Series ◽  
Deterministic Chaos ◽  
Time Series Modeling ◽  
Mathematical Methods ◽  
Car Industry ◽  
Financial Time ◽  
Low Dimensional

In last years several mathematical methods were successfully used for financial time series modeling. The main problem is to check whether irregularities of data are generated by a stochastic process or they are due to some deterministic chaos and to the presence of low-dimensional strange attractor. We focus on a test based on the correlation dimension. In particular we examine the time series of the daily closure prices of the Italian car industry "FIAT" shares.

Direct numerical simulation–based Reynolds-averaged closure for bubble-induced turbulence

2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Tian Ma ◽  
Claudio Santarelli ◽  
Thomas Ziegenhein ◽  
Dirk Lucas ◽  
Jochen Fröhlich
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Simulation Based

scholarly journals Principled approach to the selection of the embedding dimension of networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Weiwei Gu ◽  
Aditya Tandon ◽  
Yong-Yeol Ahn ◽  
Filippo Radicchi
Keyword(s):  
Real World ◽  
Structural Information ◽  
General Purpose ◽  
Embedding Dimension ◽  
Network Embedding ◽  
Machine Learning Technique ◽  
Learning Technique ◽  
Low Dimensional ◽  
Large Corpus ◽  
Selection Of

AbstractNetwork embedding is a general-purpose machine learning technique that encodes network structure in vector spaces with tunable dimension. Choosing an appropriate embedding dimension – small enough to be efficient and large enough to be effective – is challenging but necessary to generate embeddings applicable to a multitude of tasks. Existing strategies for the selection of the embedding dimension rely on performance maximization in downstream tasks. Here, we propose a principled method such that all structural information of a network is parsimoniously encoded. The method is validated on various embedding algorithms and a large corpus of real-world networks. The embedding dimension selected by our method in real-world networks suggest that efficient encoding in low-dimensional spaces is usually possible.

Numerical simulation based approach for assessment of blast induced deformation pattern in slot raise excavation

2021 ◽  
Vol 144 ◽  
pp. 104816
Author(s):  
Vivek K. Himanshu ◽  
A.K. Mishra ◽  
M.P. Roy ◽  
Ashish K. Vishwakarma ◽  
P.K. Singh
Keyword(s):  
Numerical Simulation ◽  
Deformation Pattern ◽  
Simulation Based
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