391 research outputs found
Amplitude death in coupled chaotic oscillators
Amplitude death can occur in chaotic dynamical systems with time-delay
coupling, similar to the case of coupled limit cycles. The coupling leads to
stabilization of fixed points of the subsystems. This phenomenon is quite
general, and occurs for identical as well as nonidentical coupled chaotic
systems. Using the Lorenz and R\"ossler chaotic oscillators to construct
representative systems, various possible transitions from chaotic dynamics to
fixed points are discussed.Comment: To be published in PR
Local prediction of turning points of oscillating time series
For oscillating time series, the prediction is often focused on the turning
points. In order to predict the turning point magnitudes and times it is
proposed to form the state space reconstruction only from the turning points
and modify the local (nearest neighbor) model accordingly. The model on turning
points gives optimal prediction at a lower dimensional state space than the
optimal local model applied directly on the oscillating time series and is thus
computationally more efficient. Monte Carlo simulations on different
oscillating nonlinear systems showed that it gives better predictions of
turning points and this is confirmed also for the time series of annual
sunspots and total stress in a plastic deformation experiment.Comment: 7 pages, 5 figures, 2 tables, submitted to PR
Peeling Bifurcations of Toroidal Chaotic Attractors
Chaotic attractors with toroidal topology (van der Pol attractor) have
counterparts with symmetry that exhibit unfamiliar phenomena. We investigate
double covers of toroidal attractors, discuss changes in their morphology under
correlated peeling bifurcations, describe their topological structures and the
changes undergone as a symmetry axis crosses the original attractor, and
indicate how the symbol name of a trajectory in the original lifts to one in
the cover. Covering orbits are described using a powerful synthesis of kneading
theory with refinements of the circle map. These methods are applied to a
simple version of the van der Pol oscillator.Comment: 7 pages, 14 figures, accepted to Physical Review
Isochronal synchrony and bidirectional communication with delay-coupled nonlinear oscillators
We propose a basic mechanism for isochronal synchrony and communication with
mutually delay-coupled chaotic systems. We show that two Ikeda ring oscillators
(IROs), mutually coupled with a propagation delay, synchronize isochronally
when both are symmetrically driven by a third Ikeda oscillator. This
synchronous operation, unstable in the two delay-coupled oscillators alone,
facilitates simultaneous, bidirectional communication of messages with chaotic
carrier waveforms. This approach to combine both bidirectional and
unidirectional coupling represents an application of generalized
synchronization using a mediating drive signal for a spatially distributed and
internally synchronized multi-component system
Network synchronization of groups
In this paper we study synchronized motions in complex networks in which
there are distinct groups of nodes where the dynamical systems on each node
within a group are the same but are different for nodes in different groups.
Both continuous time and discrete time systems are considered. We initially
focus on the case where two groups are present and the network has bipartite
topology (i.e., links exist between nodes in different groups but not between
nodes in the same group). We also show that group synchronous motions are
compatible with more general network topologies, where there are also
connections within the groups
Spatial patterns of desynchronization bursts in networks
We adapt a previous model and analysis method (the {\it master stability
function}), extensively used for studying the stability of the synchronous
state of networks of identical chaotic oscillators, to the case of oscillators
that are similar but not exactly identical. We find that bubbling induced
desynchronization bursts occur for some parameter values. These bursts have
spatial patterns, which can be predicted from the network connectivity matrix
and the unstable periodic orbits embedded in the attractor. We test the
analysis of bursts by comparison with numerical experiments. In the case that
no bursting occurs, we discuss the deviations from the exactly synchronous
state caused by the mismatch between oscillators
A Tool to Recover Scalar Time-Delay Systems from Experimental Time Series
We propose a method that is able to analyze chaotic time series, gained from
exp erimental data. The method allows to identify scalar time-delay systems. If
the dynamics of the system under investigation is governed by a scalar
time-delay differential equation of the form ,
the delay time and the functi on can be recovered. There are no
restrictions to the dimensionality of the chaotic attractor. The method turns
out to be insensitive to noise. We successfully apply the method to various
time series taken from a computer experiment and two different electronic
oscillators
Spin-orbit coupling and intrinsic spin mixing in quantum dots
Spin-orbit coupling effects are studied in quantum dots in InSb, a narrow-gap
material. Competition between different Rashba and Dresselhaus terms is shown
to produce wholesale changes in the spectrum. The large (and negative)
-factor and the Rashba field produce states where spin is no longer a good
quantum number and intrinsic flips occur at moderate magnetic fields. For dots
with two electrons, a singlet-triplet mixing occurs in the ground state, with
observable signatures in intraband FIR absorption, and possible importance in
quantum computation.Comment: REVTEX4 text with 3 figures (high resolution figs available by
request). Submitted to PR
Chaos and Synchronized Chaos in an Earthquake Model
We show that chaos is present in the symmetric two-block Burridge-Knopoff
model for earthquakes. This is in contrast with previous numerical studies, but
in agreement with experimental results. In this system, we have found a rich
dynamical behavior with an unusual route to chaos. In the three-block system,
we see the appearance of synchronized chaos, showing that this concept can have
potential applications in the field of seismology.Comment: To appear in Physical Review Letters (13 pages, 6 figures
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