413 research outputs found
Nonlinear projective filtering I: Background in chaos theory
We derive a locally projective noise reduction scheme for nonlinear time
series using concepts from deterministic dynamical systems, or chaos theory. We
will demonstrate its effectiveness with an example with known deterministic
dynamics and discuss methods for the verification of the results in the case of
an unknown deterministic system.Comment: 4 pages, PS figures, needs nolta.st
Nonlinear projective filtering I: Application to real time series
We discuss applications of nonlinear filtering of time series by locally
linear phase space projections. Noise can be reduced whenever the error due to
the manifold approximation is smaller than the noise in the system. Examples
include the real time extraction of the fetal electrocardiogram from abdominal
recordings.Comment: 4 pages, PS figures, needs nolta.st
Directed transport in periodically rocked random sawtooth potentials
We study directed transport of overdamped particles in a periodically rocked
random sawtooth potential. Two transport regimes can be identified which are
characterized by a nonzero value of the average velocity of particles and a
zero value, respectively. The properties of directed transport in these regimes
are investigated both analytically and numerically in terms of a random
sawtooth potential and a periodically varying driving force. Precise conditions
for the occurrence of transition between these two transport regimes are
derived and analyzed in detail.Comment: 18 pages, 7 figure
The thermodynamic cost of measurements
The measurement of thermal fluctuations provides information about the
microscopic state of a thermodynamic system and can be used in order to extract
work from a single heat bath in a suitable cyclic process. We present a minimal
framework for the modeling of a measurement device and we propose a protocol
for the measurement of thermal fluctuations. In this framework, the measurement
of thermal fluctuations naturally leads to the dissipation of work. We
illustrate this framework on a simple two states system inspired by the
Szilard's information engine
Divergence Measure Between Chaotic Attractors
We propose a measure of divergence of probability distributions for
quantifying the dissimilarity of two chaotic attractors. This measure is
defined in terms of a generalized entropy. We illustrate our procedure by
considering the effect of additive noise in the well known H\'enon attractor.
Comparison of two H\'enon attractors for slighly different parameter values,
has shown that the divergence has complex scaling structure. Finally, we show
how our approach allows to detect non-stationary events in a time series.Comment: 9 pages, 6 figure
Dynamical estimates of chaotic systems from Poincar\'e recurrences
We show that the probability distribution function that best fits the
distribution of return times between two consecutive visits of a chaotic
trajectory to finite size regions in phase space deviates from the exponential
statistics by a small power-law term, a term that represents the deterministic
manifestation of the dynamics, which can be easily experimentally detected and
theoretically estimated. We also provide simpler and faster ways to calculate
the positive Lyapunov exponents and the short-term correlation function by
either realizing observations of higher probable returns or by calculating the
eigenvalues of only one very especial unstable periodic orbit of low-period.
Finally, we discuss how our approaches can be used to treat data coming from
complex systems.Comment: subm. for publication. Accepted fpr publication in Chao
Anomalous diffusion in the citation time series of scientific publications
We analyze the citation time-series of manuscripts in three different fields of science; physics, social science and technology. The evolution of the time-series of the yearly number of citations, namely the citation trajectories, diffuse anomalously, their variance scales with time proportional to t (2H ), where H not equal 1/2. We provide detailed analysis of the various factors that lead to the anomalous behavior: non-stationarity, long-ranged correlations and a fat-tailed increment distribution. The papers exhibit a high degree of heterogeneity across the various fields, as the statistics of the highest cited papers is fundamentally different from that of the lower ones. The citation data is shown to be highly correlated and non-stationary; as all the papers except the small percentage of them with high number of citations, die out in time
Optimal Phase Description of Chaotic Oscillators
We introduce an optimal phase description of chaotic oscillations by
generalizing the concept of isochrones. On chaotic attractors possessing a
general phase description, we define the optimal isophases as Poincar\'e
surfaces showing return times as constant as possible. The dynamics of the
resultant optimal phase is maximally decoupled of the amplitude dynamics, and
provides a proper description of phase resetting of chaotic oscillations. The
method is illustrated with the R\"ossler and Lorenz systems.Comment: 10 Pages, 14 Figure
Local estimates for entropy densities in coupled map lattices
We present a method to derive an upper bound for the entropy density of
coupled map lattices with local interactions from local observations. To do
this, we use an embedding technique being a combination of time delay and
spatial embedding. This embedding allows us to identify the local character of
the equations of motion. Based on this method we present an approximate
estimate of the entropy density by the correlation integral.Comment: 4 pages, 5 figures include
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