39,611 research outputs found
An Effective chaos-based image watermarking scheme using fractal coding
AbstractThe image watermarking technology is a technique of embedding hidden data in an original image. In this paper, a new watermarking method for embedding watermark bits based on Chaos-Fractal Coding is given. A chaotic signal is defined as being deterministic, pseudo periodic and presenting sensitivity to initial conditions. Combining a chaos system with Fractal Coding plays an important role in the security, invisibility and capacity of the proposed scheme. The main idea of the new proposed algorithm for coding is to determine a set of selective blocks for steady embedding. Simulation results show that the CFC algorithm (Chaos-Fractal Coding) has a confident capacity. The embedding technique that proposed in this paper is quite general, and can be applied to the extracting scheme with demanded changes
Experimental demonstration of 25 GHz wideband chaos in symmetric dual port EDFRL
We study dynamics of chaos in dual port erbium-doped fiber ring laser (EDFRL). The laser consists of
two erbium-doped fibers, intracavity filters at 1549.30 nm, isolators, and couplers. At both ports, the laser
transitions into the chaotic regime for pump currents greater than 100 mA via period doubling route. We
calculate the Lyapunov exponents using Rosensteinâs algorithm. We obtain positive values for the largest
Lyapunov exponent (â0.2) for embedding dimensions 5, 7, 9 and 11 indicating chaos. We compute the
power spectrum of the photocurrents at the output ports of the laser. We observe a bandwidth of â 25
GHz at both ports. This ultra wideband nature of chaos obtained has potential applications in high speed
random number generation and communication
A Unified Approach to Attractor Reconstruction
In the analysis of complex, nonlinear time series, scientists in a variety of
disciplines have relied on a time delayed embedding of their data, i.e.
attractor reconstruction. The process has focused primarily on heuristic and
empirical arguments for selection of the key embedding parameters, delay and
embedding dimension. This approach has left several long-standing, but common
problems unresolved in which the standard approaches produce inferior results
or give no guidance at all. We view the current reconstruction process as
unnecessarily broken into separate problems. We propose an alternative approach
that views the problem of choosing all embedding parameters as being one and
the same problem addressable using a single statistical test formulated
directly from the reconstruction theorems. This allows for varying time delays
appropriate to the data and simultaneously helps decide on embedding dimension.
A second new statistic, undersampling, acts as a check against overly long time
delays and overly large embedding dimension. Our approach is more flexible than
those currently used, but is more directly connected with the mathematical
requirements of embedding. In addition, the statistics developed guide the user
by allowing optimization and warning when embedding parameters are chosen
beyond what the data can support. We demonstrate our approach on uni- and
multivariate data, data possessing multiple time scales, and chaotic data. This
unified approach resolves all the main issues in attractor reconstruction.Comment: 22 pages, revised version as submitted to CHAOS. Manuscript is
currently under review. 4 Figures, 31 reference
Clustering, Chaos and Crisis in a Bailout Embedding Map
We study the dynamics of inertial particles in two dimensional incompressible
flows. The particle dynamics is modelled by four dimensional dissipative
bailout embedding maps of the base flow which is represented by 2-d area
preserving maps. The phase diagram of the embedded map is rich and interesting
both in the aerosol regime, where the density of the particle is larger than
that of the base flow, as well as the bubble regime, where the particle density
is less than that of the base flow. The embedding map shows three types of
dynamic behaviour, periodic orbits, chaotic structures and mixed regions. Thus,
the embedding map can target periodic orbits as well as chaotic structures in
both the aerosol and bubble regimes at certain values of the dissipation
parameter. The bifurcation diagram of the 4-d map is useful for the
identification of regimes where such structures can be found. An attractor
merging and widening crisis is seen for a special region for the aerosols. At
the crisis, two period-10 attractors merge and widen simultaneously into a
single chaotic attractor. Crisis induced intermittency is seen at some points
in the phase diagram. The characteristic times before bursts at the crisis show
power law behaviour as functions of the dissipation parameter. Although the
bifurcation diagram for the bubbles looks similar to that of aerosols, no such
crisis regime is seen for the bubbles. Our results can have implications for
the dynamics of impurities in diverse application contexts.Comment: 16 pages, 9 figures, submitted for publicatio
Using the correlation dimension to detect non-linear dynamics: Evidence from the Athens Stock Exchange
The standardised residuals from GARCH models fitted to three stock indices of the Athens Stock Exchange are examined for evidence of chaotic behaviour. In each case the correlation dimension is calculated for a range of embedding dimensions. The results do not support the hypothesis of chaotic behaviour; it appears that each set of residuals is iid.Non-linear Dynamics, Stock Indices, Chaos, Correlation Dimension
Chaos in free electron laser oscillators
The chaotic nature of a storage-ring Free Electron Laser (FEL) is
investigated. The derivation of a low embedding dimension for the dynamics
allows the low-dimensionality of this complex system to be observed, whereas
its unpredictability is demonstrated, in some ranges of parameters, by a
positive Lyapounov exponent. The route to chaos is then explored by tuning a
single control parameter, and a period-doubling cascade is evidenced, as well
as intermittence.Comment: Accepted in EPJ
Modelling of Metallurgical Processes Using Chaos Theory and Hybrid Computational Intelligence
The main objective of the present work is to develop a framework for modelling and controlling of a real world multi-input and multi-output (MIMO) continuously drifting metallurgical process, which is shown to be a complex system. A small change in the properties of the charge composition may lead to entirely different outcome of the process. The newly emerging paradigm of soft-computing or Hybrid Computational Intelligence Systems approach which is based on neural networks, fuzzy sets, genetic algorithms and chaos theory has been applied to tackle this problem In this framework first a feed-forward neuro-model has been developed based on the data collected from a working Submerged Arc Furnace (SAF). Then the process is analysed for the existence of the chaos with the chaos theory (calculating indices like embedding dimension, Lyapunov exponent etc). After that an effort is made to evolve a fuzzy logic controller for the dynamical process using combination of genetic algorithms and the neural networks based forward model to predict the systemâs behaviour or conditions in advance and to further suggest modifications to be made to achieve the desired results
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
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