128 research outputs found
Forecasting confined spatiotemporal chaos with genetic algorithms
A technique to forecast spatiotemporal time series is presented. it uses a
Proper Ortogonal or Karhunen-Lo\`{e}ve Decomposition to encode large
spatiotemporal data sets in a few time-series, and Genetic Algorithms to
efficiently extract dynamical rules from the data. The method works very well
for confined systems displaying spatiotemporal chaos, as exemplified here by
forecasting the evolution of the onedimensional complex Ginzburg-Landau
equation in a finite domain.Comment: 4 pages, 5 figure
New way to achieve chaotic synchronization in spatially extended systems
We study the spatio-temporal behavior of simple coupled map lattices with
periodic boundary conditions. The local dynamics is governed by two maps,
namely, the sine circle map and the logistic map respectively. It is found that
even though the spatial behavior is irregular for the regularly coupled
(nearest neighbor coupling) system, the spatially synchronized (chaotic
synchronization) as well as periodic solution may be obtained by the
introduction of three long range couplings at the cost of three nearest
neighbor couplings.Comment: 5 pages (revtex), 7 figures (eps, included
Data driven optimal filtering for phase and frequency of noisy oscillations: application to vortex flowmetering
A new method for extracting the phase of oscillations from noisy time series
is proposed. To obtain the phase, the signal is filtered in such a way that the
filter output has minimal relative variation in the amplitude (MIRVA) over all
filters with complex-valued impulse response. The argument of the filter output
yields the phase. Implementation of the algorithm and interpretation of the
result are discussed. We argue that the phase obtained by the proposed method
has a low susceptibility to measurement noise and a low rate of artificial
phase slips. The method is applied for the detection and classification of mode
locking in vortex flowmeters. A novel measure for the strength of mode locking
is proposed.Comment: 12 pages, 10 figure
Generalized Phase Synchronization in unidirectionally coupled chaotic oscillators
We investigate phase synchronization between two identical or detuned
response oscillators coupled to a slightly different drive oscillator. Our
result is that phase synchronization can occur between response oscillators
when they are driven by correlated (but not identical) inputs from the drive
oscillator. We call this phenomenon Generalized Phase Synchronization (GPS) and
clarify its characteristics using Lyapunov exponents and phase difference
plots.Comment: 4 pages, 5 figure
Parameter estimation in spatially extended systems: The Karhunen-Loeve and Galerkin multiple shooting approach
Parameter estimation for spatiotemporal dynamics for coupled map lattices and
continuous time domain systems is shown using a combination of multiple
shooting, Karhunen-Loeve decomposition and Galerkin's projection methodologies.
The resulting advantages in estimating parameters have been studied and
discussed for chaotic and turbulent dynamics using small amounts of data from
subsystems, availability of only scalar and noisy time series data, effects of
space-time parameter variations, and in the presence of multiple time-scales.Comment: 11 pages, 5 figures, 4 Tables Corresponding Author - V. Ravi Kumar,
e-mail address: [email protected]
Theory and computation of covariant Lyapunov vectors
Lyapunov exponents are well-known characteristic numbers that describe growth
rates of perturbations applied to a trajectory of a dynamical system in
different state space directions. Covariant (or characteristic) Lyapunov
vectors indicate these directions. Though the concept of these vectors has been
known for a long time, they became practically computable only recently due to
algorithms suggested by Ginelli et al. [Phys. Rev. Lett. 99, 2007, 130601] and
by Wolfe and Samelson [Tellus 59A, 2007, 355]. In view of the great interest in
covariant Lyapunov vectors and their wide range of potential applications, in
this article we summarize the available information related to Lyapunov vectors
and provide a detailed explanation of both the theoretical basics and numerical
algorithms. We introduce the notion of adjoint covariant Lyapunov vectors. The
angles between these vectors and the original covariant vectors are
norm-independent and can be considered as characteristic numbers. Moreover, we
present and study in detail an improved approach for computing covariant
Lyapunov vectors. Also we describe, how one can test for hyperbolicity of
chaotic dynamics without explicitly computing covariant vectors.Comment: 21 pages, 5 figure
Synchronization of chaotic oscillator time scales
This paper deals with the chaotic oscillator synchronization. A new approach
to detect the synchronized behaviour of chaotic oscillators has been proposed.
This approach is based on the analysis of different time scales in the time
series generated by the coupled chaotic oscillators. It has been shown that
complete synchronization, phase synchronization, lag synchronization and
generalized synchronization are the particular cases of the synchronized
behavior called as "time--scale synchronization". The quantitative measure of
chaotic oscillator synchronous behavior has been proposed. This approach has
been applied for the coupled Rossler systems.Comment: 29 pages, 11 figures, published in JETP. 100, 4 (2005) 784-79
An Alternative Method to Deduce Bubble Dynamics in Single Bubble Sonoluminescence Experiments
In this paper we present an experimental approach that allows to deduce the
important dynamical parameters of single sonoluminescing bubbles (pressure
amplitude, ambient radius, radius-time curve) The technique is based on a few
previously confirmed theoretical assumptions and requires the knowledge of
quantities such as the amplitude of the electric excitation and the phase of
the flashes in the acoustic period. These quantities are easily measurable by a
digital oscilloscope, avoiding the cost of expensive lasers, or ultrafast
cameras of previous methods. We show the technique on a particular example and
compare the results with conventional Mie scattering. We find that within the
experimental uncertainties these two techniques provide similar results.Comment: 8 pages, 5 figures, submitted to Phys. Rev.
Physics and Applications of Laser Diode Chaos
An overview of chaos in laser diodes is provided which surveys experimental
achievements in the area and explains the theory behind the phenomenon. The
fundamental physics underpinning this behaviour and also the opportunities for
harnessing laser diode chaos for potential applications are discussed. The
availability and ease of operation of laser diodes, in a wide range of
configurations, make them a convenient test-bed for exploring basic aspects of
nonlinear and chaotic dynamics. It also makes them attractive for practical
tasks, such as chaos-based secure communications and random number generation.
Avenues for future research and development of chaotic laser diodes are also
identified.Comment: Published in Nature Photonic
Comparison of the bifurcation scenarios predicted by the single-mode and multimode semiconductor laser rate equations
We present a detailed comparison of the bifurcation scenarios predicted by single-mode and multimode semiconductor laser rate equation models under large amplitude injection current modulation. The influence of the gain model on the predicted dynamics is investigated. Calculations of the dependence of the time averaged longitudinal mode intensities on modulation frequency are compared with experiments performed on an AlxGa1-xAs Fabry-Pérot semiconductor laser.K. A. Corbett and M. W. Hamilto
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