3,884 research outputs found
Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
We investigate a generalised version of the recently proposed ordinal
partition time series to network transformation algorithm. Firstly we introduce
a fixed time lag for the elements of each partition that is selected using
techniques from traditional time delay embedding. The resulting partitions
define regions in the embedding phase space that are mapped to nodes in the
network space. Edges are allocated between nodes based on temporal succession
thus creating a Markov chain representation of the time series. We then apply
this new transformation algorithm to time series generated by the R\"ossler
system and find that periodic dynamics translate to ring structures whereas
chaotic time series translate to band or tube-like structures -- thereby
indicating that our algorithm generates networks whose structure is sensitive
to system dynamics. Furthermore we demonstrate that simple network measures
including the mean out degree and variance of out degrees can track changes in
the dynamical behaviour in a manner comparable to the largest Lyapunov
exponent. We also apply the same analysis to experimental time series generated
by a diode resonator circuit and show that the network size, mean shortest path
length and network diameter are highly sensitive to the interior crisis
captured in this particular data set
Detecting chaos in particle accelerators through the frequency map analysis method
The motion of beams in particle accelerators is dominated by a plethora of
non-linear effects which can enhance chaotic motion and limit their
performance. The application of advanced non-linear dynamics methods for
detecting and correcting these effects and thereby increasing the region of
beam stability plays an essential role during the accelerator design phase but
also their operation. After describing the nature of non-linear effects and
their impact on performance parameters of different particle accelerator
categories, the theory of non-linear particle motion is outlined. The recent
developments on the methods employed for the analysis of chaotic beam motion
are detailed. In particular, the ability of the frequency map analysis method
to detect chaotic motion and guide the correction of non-linear effects is
demonstrated in particle tracking simulations but also experimental data.Comment: Submitted for publication in Chaos, Focus Issue: Chaos Detection
Methods and Predictabilit
Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones. Part I
Ultra low frequency, kHz and MHz electromagnetic anomalies were recorded
prior to the L'Aquila catastrophic earthquake that occurred on April 6, 2009.
The main aims of this contribution are: (i) To suggest a procedure for the
designation of detected EM anomalies as seismogenic ones. We do not expect to
be possible to provide a succinct and solid definition of a pre-seismic EM
emission. Instead, we attempt, through a multidisciplinary analysis, to provide
elements of a definition. (ii) To link the detected MHz and kHz EM anomalies
with equivalent last stages of the L'Aquila earthquake preparation process.
(iii) To put forward physically meaningful arguments to support a way of
quantifying the time to global failure and the identification of distinguishing
features beyond which the evolution towards global failure becomes
irreversible. The whole effort is unfolded in two consecutive parts. We clarify
we try to specify not only whether or not a single EM anomaly is pre-seismic in
itself, but mainly whether a combination of kHz, MHz, and ULF EM anomalies can
be characterized as pre-seismic one
Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part two: Solar Flares dynamics
In the second part of this study and similarly with part one, the nonlinear
analysis of the solar flares index is embedded in the non-extensive statistical
theory of Tsallis [1]. The triplet of Tsallis, as well as the correlation
dimension and the Lyapunov exponent spectrum were estimated for the SVD
components of the solar flares timeseries. Also the multifractal scaling
exponent spectrum, the generalized Renyi dimension spectrum and the spectrum of
the structure function exponents were estimated experimentally and
theoretically by using the entropy principle included in Tsallis non extensive
statistical theory, following Arimitsu and Arimitsu [2]. Our analysis showed
clearly the following: a) a phase transition process in the solar flare
dynamics from high dimensional non Gaussian SOC state to a low dimensional also
non Gaussian chaotic state, b) strong intermittent solar corona turbulence and
anomalous (multifractal) diffusion solar corona process, which is strengthened
as the solar corona dynamics makes phase transition to low dimensional chaos:
c) faithful agreement of Tsallis non equilibrium statistical theory with the
experimental estimations of i) non-Gaussian probability distribution function,
ii) multifractal scaling exponent spectrum and generalized Renyi dimension
spectrum, iii) exponent spectrum of the structure functions estimated for the
sunspot index and its underlying non equilibrium solar dynamics. e) The solar
flare dynamical profile is revealed similar to the dynamical profile of the
solar convection zone as far as the phase transition process from SOC to chaos
state. However the solar low corona (solar flare) dynamical characteristics can
be clearly discriminated from the dynamical characteristics of the solar
convection zone.Comment: 21 pages, 11 figures, 1 table. arXiv admin note: substantial text
overlap with arXiv:1201.649
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