194 research outputs found
Random Delays and the Synchronization of Chaotic Maps
We investigate the dynamics of an array of logistic maps coupled with random
delay times. We report that for adequate coupling strength the array is able to
synchronize, in spite of the random delays. Specifically, we find that the
synchronized state is a homogeneous steady-state, where the chaotic dynamics of
the individual maps is suppressed. This differs drastically from the
synchronization with instantaneous and fixed-delay coupling, as in those cases
the dynamics is chaotic. Also in contrast with the instantaneous and
fixed-delay cases, the synchronization does not dependent on the connection
topology, depends only on the average number of links per node. We find a
scaling law that relates the distance to synchronization with the randomness of
the delays. We also carry out a statistical linear stability analysis that
confirms the numerical results and provides a better understanding of the
nontrivial roles of random delayed interactions.Comment: 5 pages, 5 figure
Inferring long memory processes in the climate network via ordinal pattern analysis
We use ordinal patterns and symbolic analysis to construct global climate
networks and uncover long and short term memory processes. The data analyzed is
the monthly averaged surface air temperature (SAT field) and the results
suggest that the time variability of the SAT field is determined by patterns of
oscillatory behavior that repeat from time to time, with a periodicity related
to intraseasonal oscillations and to El Ni\~{n}o on seasonal-to-interannual
time scales.Comment: 10 pages, 13 figures Enlarged version, new sections and figures.
Accepted in Chao
Anticipating the dynamics of chaotic maps
We study the regime of anticipated synchronization in unidirectionally
coupled chaotic maps such that the slave map has its own output reinjected
after a certain delay. For a class of simple maps, we give analytic conditions
for the stability of the synchronized solution, and present results of
numerical simulations of coupled 1D Bernoulli-like maps and 2D Baker maps, that
agree well with the analytic predictions.Comment: Uses the elsart.cls (v2000) style (included). 9 pages, including 4
figures. New version contains minor modifications to text and figure
Emergence of spike correlations in periodically forced excitable systems
In sensory neurons the presence of noise can facilitate the detection of weak
information-carrying signals, which are encoded and transmitted via correlated
sequences of spikes. Here we investigate relative temporal order in spike
sequences induced by a subthreshold periodic input, in the presence of white
Gaussian noise. To simulate the spikes, we use the FitzHugh-Nagumo model, and
to investigate the output sequence of inter-spike intervals (ISIs), we use the
symbolic method of ordinal analysis. We find different types of relative
temporal order, in the form of preferred ordinal patterns which depend on both,
the strength of the noise and the period of the input signal. We also
demonstrate a resonance-like behavior, as certain periods and noise levels
enhance temporal ordering in the ISI sequence, maximizing the probability of
the preferred patterns. Our findings could be relevant for understanding the
mechanisms underlying temporal coding, by which single sensory neurons
represent in spike sequences the information about weak periodic stimuli
Numerical and experimental study of the effects of noise on the permutation entropy
We analyze the effects of noise on the permutation entropy of dynamical
systems. We take as numerical examples the logistic map and the R\"ossler
system. Upon varying the noise strengthfaster, we find a transition from an
almost-deterministic regime, where the permutation entropy grows slower than
linearly with the pattern dimension, to a noise-dominated regime, where the
permutation entropy grows faster than linearly with the pattern dimension. We
perform the same analysis on experimental time-series by considering the
stochastic spiking output of a semiconductor laser with optical feedback.
Because of the experimental conditions, the dynamics is found to be always in
the noise-dominated regime. Nevertheless, the analysis allows to detect
regularities of the underlying dynamics. By comparing the results of these
three different examples, we discuss the possibility of determining from a time
series whether the underlying dynamics is dominated by noise or not
Characterization of the anticipated synchronization regime in the coupled FitzHugh--Nagumo model for neurons
We characterize numerically the regime of anticipated synchronization in the
coupled FitzHugh-Nagumo model for neurons. We consider two neurons, coupled
unidirectionally (in a master-slave configuration), subject to the same random
external forcing and with a recurrent inhibitory delayed connection in the
slave neuron. We show that the scheme leads to anticipated synchronization, a
regime in which the slave neuron fires the same train of pulses as the master
neuron, but earlier in time. We characterize the synchronization in the
parameter space (coupling strength, anticipation time) and introduce several
quantities to measure the degree of synchronization.Comment: 8 pages. Proceedings of the conference on "Stochastic Systems: From
Randomness to"Complexit
Inverse Anticipating Synchronization
We report a new type of chaos synchronization:inverse anticipating
synchronization, where a time delay chaotic system can drive another system in
such a way that the driven system anticipates the driver by synchronizing with
its inverse future state. We extend the concept of inverse anticipating chaos
synchronization to cascaded systems. We propose means for the experimental
observation of inverse anticipating chaos synchronization in external cavity
lasers.Comment: LaTex 6 pages, resubmitted to PR
Anticipating the response of excitable systems driven by random forcing
We study the regime of anticipated synchronization in unidirectionally
coupled model neurons subject to a common external aperiodic forcing that makes
their behavior unpredictable. We show numerically and by implementation in
analog hardware electronic circuits that, under appropriate coupling
conditions, the pulses fired by the slave neuron anticipate (i.e. predict) the
pulses fired by the master neuron. This anticipated synchronization occurs even
when the common external forcing is white noise.Comment: 12 pages (RevTex format
Crowd synchrony and quorum sensing in delay-coupled lasers
Crowd synchrony and quorum sensing arise when a large number of dynamical
elements communicate with each other via a common information pool. Previous
evidence in different fields, including chemistry, biology and civil
engineering, has shown that this type of coupling leads to synchronization,
when coupling is instantaneous and the number of coupled elements is large
enough. Here we consider a situation in which the transmission of information
between the system components and the coupling pool is not instantaneous. To
that end, we model a system of semiconductor lasers optically coupled to a
central laser with a delay. Our results show that, even though the lasers are
non-identical due to their distinct optical frequencies, zero-lag
synchronization arises. By changing a system parameter, we can switch between
two different types of synchronization transition. The dependence of the
transition with respect to the delay-coupling parameters is studied.Comment: 4 pages, 4 figure
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