2,028 research outputs found
Disturbing synchronization: Propagation of perturbations in networks of coupled oscillators
We study the response of an ensemble of synchronized phase oscillators to an
external harmonic perturbation applied to one of the oscillators. Our main goal
is to relate the propagation of the perturbation signal to the structure of the
interaction network underlying the ensemble. The overall response of the system
is resonant, exhibiting a maximum when the perturbation frequency coincides
with the natural frequency of the phase oscillators. The individual response,
on the other hand, can strongly depend on the distance to the place where the
perturbation is applied. For small distances on a random network, the system
behaves as a linear dissipative medium: the perturbation propagates at constant
speed, while its amplitude decreases exponentially with the distance. For
larger distances, the response saturates to an almost constant level. These
different regimes can be analytically explained in terms of the length
distribution of the paths that propagate the perturbation signal. We study the
extension of these results to other interaction patterns, and show that
essentially the same phenomena are observed in networks of chaotic oscillators.Comment: To appear in Eur. Phys. J.
Synchronization framework for modeling transition to thermoacoustic instability in laminar combustors
We, herein, present a new model based on the framework of synchronization to
describe a thermoacoustic system and capture the multiple bifurcations that
such a system undergoes. Instead of applying flame describing function to
depict the unsteady heat release rate as the flame's response to acoustic
perturbation, the new model considers the acoustic field and the unsteady heat
release rate as a pair of nonlinearly coupled damped oscillators. By varying
the coupling strength, multiple dynamical behaviors, including limit cycle
oscillation, quasi-periodic oscillation, strange nonchaos, and chaos can be
captured. Furthermore, the model was able to qualitatively replicate the
different behaviors of a laminar thermoacoustic system observed in experiments
by Kabiraj et al.~[Chaos 22, 023129 (2012)]. By analyzing the temporal
variation of the phase difference between heat release rate oscillations and
pressure oscillations under different dynamical states, we show that the
characteristics of the dynamical states depend on the nature of synchronization
between the two signals, which is consistent with previous experimental
findings.Comment: 18 pages, 7 figure
Realizing the physics of motile cilia synchronization with driven colloids
Cilia and flagella in biological systems often show large scale cooperative
behaviors such as the synchronization of their beats in "metachronal waves".
These are beautiful examples of emergent dynamics in biology, and are essential
for life, allowing diverse processes from the motility of eukaryotic
microorganisms, to nutrient transport and clearance of pathogens from mammalian
airways. How these collective states arise is not fully understood, but it is
clear that individual cilia interact mechanically,and that a strong and long
ranged component of the coupling is mediated by the viscous fluid. We review
here the work by ourselves and others aimed at understanding the behavior of
hydrodynamically coupled systems, and particularly a set of results that have
been obtained both experimentally and theoretically by studying actively driven
colloidal systems. In these controlled scenarios, it is possible to selectively
test aspects of the living motile cilia, such as the geometrical arrangement,
the effects of the driving profile and the distance to no-slip boundaries. We
outline and give examples of how it is possible to link model systems to
observations on living systems, which can be made on microorganisms, on cell
cultures or on tissue sections. This area of research has clear clinical
application in the long term, as severe pathologies are associated with
compromised cilia function in humans.Comment: 31 pages, to appear in Annual Review of Condensed Matter Physic
Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks
The role of restorative coupling on synchronization of coupled identical
harmonic oscillators is studied. Necessary and sufficient conditions, under
which the individual systems' solutions converge to a common trajectory, are
presented. Through simple physical examples, the meaning and limitations of the
theorems are expounded. Also, to demonstrate their versatility, the results are
extended to cover LTI passive electrical networks. One of the extensions
generalizes the well-known link between the asymptotic stability of the
synchronization subspace and the second smallest eigenvalue of the Laplacian
matrix.Comment: 13 pages, 8 figure
Quantum correlations and synchronization measures
The phenomenon of spontaneous synchronization is universal and only recently
advances have been made in the quantum domain. Being synchronization a kind of
temporal correlation among systems, it is interesting to understand its
connection with other measures of quantum correlations. We review here what is
known in the field, putting emphasis on measures and indicators of
synchronization which have been proposed in the literature, and comparing their
validity for different dynamical systems, highlighting when they give similar
insights and when they seem to fail.Comment: book chapter, 18 pages, 7 figures, Fanchini F., Soares Pinto D.,
Adesso G. (eds) Lectures on General Quantum Correlations and their
Applications. Quantum Science and Technology. Springer (2017
Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains
Synchronization cluster analysis is an approach to the detection of
underlying structures in data sets of multivariate time series, starting from a
matrix R of bivariate synchronization indices. A previous method utilized the
eigenvectors of R for cluster identification, analogous to several recent
attempts at group identification using eigenvectors of the correlation matrix.
All of these approaches assumed a one-to-one correspondence of dominant
eigenvectors and clusters, which has however been shown to be wrong in
important cases. We clarify the usefulness of eigenvalue decomposition for
synchronization cluster analysis by translating the problem into the language
of stochastic processes, and derive an enhanced clustering method harnessing
recent insights from the coarse-graining of finite-state Markov processes. We
illustrate the operation of our method using a simulated system of coupled
Lorenz oscillators, and we demonstrate its superior performance over the
previous approach. Finally we investigate the question of robustness of the
algorithm against small sample size, which is important with regard to field
applications.Comment: Follow-up to arXiv:0706.3375. Journal submission 9 Jul 2007.
Published 19 Dec 200
Color Image Segmentation Based on Modified Kuramoto Model
AbstractA new approach for color image segmentation is proposed based on Kuramoto model in this paper. Firstly, the classic Kuramoto model which describes a global coupled oscillator network is changed to be one that is locally coupled to simulate the neuron activity in visual cortex and to describe the influence for phase changing by external stimuli. Secondly, a rebuilt method of coupled neuron activities is proposed by introducing and computing instantaneous frequency. Three oscillating curves corresponding to the pixel values of R, G, B for color image are formed by the coupled network and are added up to produce the superposition of oscillation. Finally, color images are segmented according to the synchronization of the oscillating superposition by extracting and checking the frequency of the oscillating curves. The performance is compared with that from other representative segmentation approaches
Synchronization of small oscillations
Synchronization is studied in an array of identical oscillators undergoing
small vibrations. The overall coupling is described by a pair of
matrix-weighted Laplacian matrices; one representing the dissipative, the other
the restorative connectors. A construction is proposed to combine these two
real matrices in a single complex matrix. It is shown that whether the
oscillators synchronize in the steady state or not depends on the number of
eigenvalues of this complex matrix on the imaginary axis. Certain refinements
of this condition for the special cases, where the restorative coupling is
either weak or absent, are also presented.Comment: 16 pages, 6 figure
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