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.

DETERMINISTIC CHAOS IN SOUNDS OF ASIAN CICADAS

2006 ◽  
Vol 14 (04) ◽  
pp. 555-566 ◽  
Author(s):  
TINA P. BENKO ◽  
MATJAŽ PERC
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Sound Production ◽  
Deterministic Chaos ◽  
Nonlinear Time Series ◽  
Nonlinear Time Series Analysis ◽  
Maximal Lyapunov Exponent ◽  
Sound Recording ◽  
Series Analysis ◽  
Production Mechanisms

We analyze the sound recording of the Southeast Asian cicada Tosena depicta with methods of nonlinear time series analysis. First, we reconstruct the phase space from the sound recording and test it against determinism and stationarity. After positively establishing determinism and stationarity in the series, we calculate the maximal Lyapunov exponent. We find that the latter is positive, from which we conclude that the sound recording possesses clear markers of deterministic chaos. We discuss that methods of nonlinear time series analysis can yield instructive insights and foster the understanding of acoustic and vibrational communication among insects, as well as provide vital clues regarding the origin and functionality of their sound production mechanisms. Furthermore, such studies can serve as means to distinguish different insect genera or even species either from each other or under various environmental influences.

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 Pattern identification in dynamical systems via symbolic time series analysis

2007 ◽  
Vol 40 (11) ◽  
pp. 2897-2907 ◽  
Author(s):  
Venkatesh Rajagopalan ◽  
Asok Ray ◽  
Rohan Samsi ◽  
Jeffrey Mayer
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Analysis ◽  
Pattern Identification ◽  
Series Analysis ◽  
Symbolic Time Series Analysis

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.

Online Discovery and Classification of Operational Regimes From an Ensemble of Time Series Data

2020 ◽  
Vol 142 (11) ◽  
Author(s):  
Chandrachur Bhattacharya ◽  
Asok Ray
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Time Series Analysis ◽  
Time Series Data ◽  
Real Life ◽  
Series Data ◽  
Markov Modeling ◽  
Stable Regime ◽  
Series Analysis ◽  
Symbolic Time Series Analysis

Abstract One of the pertinent problems in decision and control of dynamical systems is to identify the current operational regime of the physical process under consideration. To this end, there has been an upsurge in (data-driven) machine learning methods, such as symbolic time series analysis, hidden Markov modeling, and artificial neural networks, which often rely on some form of supervised learning based on preclassified data to construct the classifier. However, this approach may not be adequate for dynamical systems with a variety of operational regimes and possible anomalous/failure conditions. To address this issue, the technical brief proposes a methodology, built upon the concept of symbolic time series analysis, wherein the classifier learns to discover the patterns so that the algorithms can train themselves online while simultaneously functioning as a classifier. The efficacy of the methodology is demonstrated on time series of: (i) synthetic data from an unforced Van der Pol equation and (ii) pressure oscillation data from an experimental Rijke tube apparatus that emulates the thermoacoustics in real-life combustors where the process dynamics undergoes changes from the stable regime to an unstable regime and vice versa via transition to transient regimes. The underlying algorithms are capable of accurately learning and capturing the various regimes online in a (primarily) unsupervised manner.

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