144 research outputs found
Synchronization of Random Linear Maps
We study synchronization of random one-dimensional linear maps for which the
Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of
these maps are explained using their relation with a random walk. We confirm
that the Lyapunov exponent changes sign at the complete synchronization
transition. We also consider partial synchronization of nonidentical systems.
It turns out that the way partial synchronization manifests depends on the type
of differences (in Lyapunov exponent or in contraction points) between the
systems. The crossover from partial synchronization to complete synchronization
is also examined.Comment: 5 pages, 6 figure
Frequency and phase synchronization of two coupled neurons with channel noise
We study the frequency and phase synchronization in two coupled identical and
nonidentical neurons with channel noise. The occupation number method is used
to model the neurons in the context of stochastic Hodgkin-Huxley model in which
the strength of of channel noise is represented by ion channel cluster size of
the initiation region of neuron. It is shown that frequency synchronization
only was achieved at arbitrary value of couple strength as long as two neurons'
channel cluster sizes are the same. We also show that the relative phase of
neurons can display profuse dynamic behavior under the combined action of
coupling and channel noise. Both qualitative and quantitative descriptions are
applied to describe the transitions between those behaviors. Relevance of our
findings to controlling neural synchronization experimentally is discussed.Comment: 8 pages, 10 figure
On the relationship between directed percolation and the synchronization transition in spatially extended systems
We study the nature of the synchronization transition in spatially extended
systems by discussing a simple stochastic model. An analytic argument is put
forward showing that, in the limit of discontinuous processes, the transition
belongs to the directed percolation (DP) universality class. The analysis is
complemented by a detailed investigation of the dependence of the first passage
time for the amplitude of the difference field on the adopted threshold. We
find the existence of a critical threshold separating the regime controlled by
linear mechanisms from that controlled by collective phenomena. As a result of
this analysis we conclude that the synchronization transition belongs to the DP
class also in continuous models. The conclusions are supported by numerical
checks on coupled map lattices too
Transition to Stochastic Synchronization in Spatially Extended Systems
Spatially extended dynamical systems, namely coupled map lattices, driven by
additive spatio-temporal noise are shown to exhibit stochastic synchronization.
In analogy with low-dymensional systems, synchronization can be achieved only
if the maximum Lyapunov exponent becomes negative for sufficiently large noise
amplitude. Moreover, noise can suppress also the non-linear mechanism of
information propagation, that may be present in the spatially extended system.
A first example of phase transition is observed when both the linear and the
non-linear mechanisms of information production disappear at the same critical
value of the noise amplitude. The corresponding critical properties can be
hardly identified numerically, but some general argument suggests that they
could be ascribed to the Kardar-Parisi-Zhang universality class. Conversely,
when the non-linear mechanism prevails on the linear one, another type of phase
transition to stochastic synchronization occurs. This one is shown to belong to
the universality class of directed percolation.Comment: 21 pages, Latex - 14 EPS Figs - To appear on Physical Review
Correlation property of length sequences based on global structure of complete genome
This paper considers three kinds of length sequences of the complete genome.
Detrended fluctuation analysis, spectral analysis, and the mean distance
spanned within time are used to discuss the correlation property of these
sequences. The values of the exponents from these methods of these three kinds
of length sequences of bacteria indicate that the long-range correlations exist
in most of these sequences. The correlation have a rich variety of behaviours
including the presence of anti-correlations. Further more, using the exponent
, it is found that these correlations are all linear (). It is also found that these sequences exhibit noise in some
interval of frequency (). The length of this interval of frequency depends
on the length of the sequence. The shape of the periodogram in exhibits
some periodicity. The period seems to depend on the length and the complexity
of the length sequence.Comment: RevTex, 9 pages with 5 figures and 3 tables. Phys. Rev. E Jan. 1,2001
(to appear
Random Amino Acid Mutations and Protein Misfolding Lead to Shannon Limit in Sequence-Structure Communication
The transmission of genomic information from coding sequence to protein structure during protein synthesis is subject to stochastic errors. To analyze transmission limits in the presence of spurious errors, Shannon's noisy channel theorem is applied to a communication channel between amino acid sequences and their structures established from a large-scale statistical analysis of protein atomic coordinates. While Shannon's theorem confirms that in close to native conformations information is transmitted with limited error probability, additional random errors in sequence (amino acid substitutions) and in structure (structural defects) trigger a decrease in communication capacity toward a Shannon limit at 0.010 bits per amino acid symbol at which communication breaks down. In several controls, simulated error rates above a critical threshold and models of unfolded structures always produce capacities below this limiting value. Thus an essential biological system can be realistically modeled as a digital communication channel that is (a) sensitive to random errors and (b) restricted by a Shannon error limit. This forms a novel basis for predictions consistent with observed rates of defective ribosomal products during protein synthesis, and with the estimated excess of mutual information in protein contact potentials
How to Achieve Fast Entrainment? The Timescale to Synchronization
Entrainment, where oscillators synchronize to an external signal, is ubiquitous in nature. The transient time leading to entrainment plays a major role in many biological processes. Our goal is to unveil the specific dynamics that leads to fast entrainment. By studying a generic model, we characterize the transient time to entrainment and show how it is governed by two basic properties of an oscillator: the radial relaxation time and the phase velocity distribution around the limit cycle. Those two basic properties are inherent in every oscillator. This concept can be applied to many biological systems to predict the average transient time to entrainment or to infer properties of the underlying oscillator from the observed transients. We found that both a sinusoidal oscillator with fast radial relaxation and a spike-like oscillator with slow radial relaxation give rise to fast entrainment. As an example, we discuss the jet-lag experiments in the mammalian circadian pacemaker
Mechanisms Behind the Generalized Synchronization Conditions
A universal mechanism underlying generalized synchronization conditions in
unidirectionally coupled stochastic oscillators is considered. The
consideration is carried out in the framework of a modified system with
additional dissipation. The approach developed is illustrated with model
examples. The conclusion is reached that two types of the behavior of nonlinear
dynamic systems known as generalized synchronization and noise-induced
synchronization, which are viewed as different phenomena, actually represent a
unique type of the synchronous behavior of stochastic oscillators and are
caused by the same mechanism.Comment: 8 pages, 5 figure
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