14,088 research outputs found
Recurrence plot statistics and the effect of embedding
Recurrence plots provide a graphical representation of the recurrent patterns
in a timeseries, the quantification of which is a relatively new field. Here we
derive analytical expressions which relate the values of key statistics,
notably determinism and entropy of line length distribution, to the correlation
sum as a function of embedding dimension. These expressions are obtained by
deriving the transformation which generates an embedded recurrence plot from an
unembedded plot. A single unembedded recurrence plot thus provides the
statistics of all possible embedded recurrence plots. If the correlation sum
scales exponentially with embedding dimension, we show that these statistics
are determined entirely by the exponent of the exponential. This explains the
results of Iwanski and Bradley (Chaos 8 [1998] 861-871) who found that certain
recurrence plot statistics are apparently invariant to embedding dimension for
certain low-dimensional systems. We also examine the relationship between the
mutual information content of two timeseries and the common recurrent structure
seen in their recurrence plots. This allows time-localized contributions to
mutual information to be visualized. This technique is demonstrated using
geomagnetic index data; we show that the AU and AL geomagnetic indices share
half their information, and find the timescale on which mutual features appear
Organization of the magnetosphere during substorms
The change in degree of organization of the magnetosphere during substorms is
investigated by analyzing various geomagnetic indices, as well as
interplanetary magnetic field z-component and solar wind flow speed. We
conclude that the magnetosphere self-organizes globally during substorms, but
neither the magnetosphere nor the solar wind become more predictable in the
course of a substorm. This conclusion is based on analysis of five hundred
substorms in the period from 2000 to 2002. A minimal dynamic-stochastic model
of the driven magnetosphere that reproduces many statistical features of
substorm indices is discussed
Attractor reconstruction of an impact oscillator for parameter identification
Peer reviewedPreprin
Detecting Determinism in High Dimensional Chaotic Systems
A method based upon the statistical evaluation of the differentiability of
the measure along the trajectory is used to identify in high dimensional
systems. The results show that the method is suitable for discriminating
stochastic from deterministic systems even if the dimension of the latter is as
high as 13. The method is shown to succeed in identifying determinism in
electro-encephalogram signals simulated by means of a high dimensional system.Comment: 8 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E
(25 apr 2001
How to avoid potential pitfalls in recurrence plot based data analysis
Recurrence plots and recurrence quantification analysis have become popular
in the last two decades. Recurrence based methods have on the one hand a deep
foundation in the theory of dynamical systems and are on the other hand
powerful tools for the investigation of a variety of problems. The increasing
interest encompasses the growing risk of misuse and uncritical application of
these methods. Therefore, we point out potential problems and pitfalls related
to different aspects of the application of recurrence plots and recurrence
quantification analysis
Incompleteness of relational simulations in the blocking paradigm
Refinement is the notion of development between formal specifications For specifications given in a relational formalism downward and upward simulations are the standard method to verify that a refinement holds their usefulness based upon their soundness and joint completeness This is known to be true for total relational specifications and has been claimed to hold for partial relational specifications in both the non-blocking and blocking interpretations
In this paper we show that downward and upward simulations in the blocking interpretation where domains are guards are not Jointly complete This contradicts earlier claims in the literature We illustrate this with an example (based on one recently constructed by Reeves and Streader) and then construct a proof to show why Joint completeness fails in general (C) 2010 Elsevier B V All rights reserve
The dynamics of laser droplet generation
We propose an experimental setup allowing for the characterization of laser
droplet generation in terms of the underlying dynamics, primarily showing that
the latter is deterministically chaotic by means of nonlinear time series
analysis methods. In particular, we use a laser pulse to melt the end of a
properly fed vertically placed metal wire. Due to the interplay of surface
tension, gravity force and light-metal interaction, undulating pendant droplets
are formed at the molten end, which eventually completely detach from the wire
as a consequence of their increasing mass. We capture the dynamics of this
process by employing a high-speed infrared camera, thereby indirectly measuring
the temperature of the wire end and the pendant droplets. The time series is
subsequently generated as the mean value over the pixel intensity of every
infrared snapshot. Finally, we employ methods of nonlinear time series analysis
to reconstruct the phase space from the observed variable and test it against
determinism and stationarity. After establishing that the observed laser
droplet generation is a deterministic and dynamically stationary process, we
calculate the spectra of Lyapunov exponents. We obtain a positive largest
Lyapunov exponent and a negative divergence, i.e., sum of all the exponents,
thus indicating that the observed dynamics is deterministically chaotic with an
attractor as solution in the phase space. In addition to characterizing the
dynamics of laser droplet generation, we outline industrial applications of the
process and point out the significance of our findings for future attempts at
mathematical modeling.Comment: 7 two-column pages, 8 figures; accepted for publication in Chaos
[supplementary material available at
http://www.matjazperc.com/chaos/laser.html
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