23 research outputs found
Synchronization and resonance in a driven system of coupled oscillators
We study the noise effects in a driven system of globally coupled
oscillators, with particular attention to the interplay between driving and
noise. The self-consistency equation for the order parameter, which measures
the collective synchronization of the system, is derived; it is found that the
total order parameter decreases monotonically with noise, indicating overall
suppression of synchronization. Still, for large coupling strengths, there
exists an optimal noise level at which the periodic (ac) component of the order
parameter reaches its maximum. The response of the phase velocity is also
examined and found to display resonance behavior.Comment: 17 pages, 3 figure
Phase synchronization and noise-induced resonance in systems of coupled oscillators
We study synchronization and noise-induced resonance phenomena in systems of
globally coupled oscillators, each possessing finite inertia. The behavior of
the order parameter, which measures collective synchronization of the system,
is investigated as the noise level and the coupling strength are varied, and
hysteretic behavior is manifested. The power spectrum of the phase velocity is
also examined and the quality factor as well as the response function is
obtained to reveal noise-induced resonance behavior.Comment: to be published in Phys. Rev.
Role of delay in the mechanism of cluster formation
We study the role of delay in phase synchronization and phenomena responsible
for cluster formation in delayed coupled maps on various networks. Using
numerical simulations, we demonstrate that the presence of delay may change the
mechanism of unit to unit interaction. At weak coupling values, same parity
delays are associated with the same phenomenon of cluster formation and exhibit
similar dynamical evolution. Intermediate coupling values yield rich
delay-induced driven cluster patterns. A Lyapunov function analysis sheds light
on the robustness of the driven clusters observed for delayed bipartite
networks. Our results reveal that delay may lead to a completely different
relation, between dynamical and structural clusters, than observed for the
undelayed case.Comment: 4+ pages, 4 figues, PRE Rapid Communication (in press
A Model of an Oscillatory Neural Network with Multilevel Neurons for Pattern Recognition and Computing
The current study uses a novel method of multilevel neurons and high order
synchronization effects described by a family of special metrics, for pattern
recognition in an oscillatory neural network (ONN). The output oscillator
(neuron) of the network has multilevel variations in its synchronization value
with the reference oscillator, and allows classification of an input pattern
into a set of classes. The ONN model is implemented on thermally-coupled
vanadium dioxide oscillators. The ONN is trained by the simulated annealing
algorithm for selection of the network parameters. The results demonstrate that
ONN is capable of classifying 512 visual patterns (as a cell array 3 * 3,
distributed by symmetry into 102 classes) into a set of classes with a maximum
number of elements up to fourteen. The classification capability of the network
depends on the interior noise level and synchronization effectiveness
parameter. The model allows for designing multilevel output cascades of neural
networks with high net data throughput. The presented method can be applied in
ONNs with various coupling mechanisms and oscillator topology.Comment: 26 pages, 24 figure
Heterogeneous delays making parents synchronized: A coupled maps on Cayley tree model
We study the phase synchronized clusters in the diffusively coupled maps on
the Cayley tree networks for heterogeneous delay values. Cayley tree networks
comprise of two parts: the inner nodes and the boundary nodes. We find that
heterogeneous delays lead to various cluster states, such as; (a) cluster state
consisting of inner nodes and boundary nodes, and (b) cluster state consisting
of only boundary nodes. The former state may comprise of nodes from all the
generations forming self-organized cluster or nodes from few generations
yielding driven clusters depending upon on the parity of heterogeneous delay
values. Furthermore, heterogeneity in delays leads to the lag synchronization
between the siblings lying on the boundary by destroying the exact
synchronization among them. The time lag being equal to the difference in the
delay values. The Lyapunov function analysis sheds light on the destruction of
the exact synchrony among the last generation nodes. To the end we discuss the
relevance of our results with respect to their applications in the family
business as well as in understanding the occurrence of genetic diseases.Comment: 9 pages, 11 figure
Bounding network spectra for network design
The identification of the limiting factors in the dynamical behavior of
complex systems is an important interdisciplinary problem which often can be
traced to the spectral properties of an underlying network. By deriving a
general relation between the eigenvalues of weighted and unweighted networks,
here I show that for a wide class of networks the dynamical behavior is tightly
bounded by few network parameters. This result provides rigorous conditions for
the design of networks with predefined dynamical properties and for the
structural control of physical processes in complex systems. The results are
illustrated using synchronization phenomena as a model process.Comment: 17 pages, 4 figure
Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks
We show that an introduction of a phase parameter (), with , in the interlayer coupling terms of multiplex networks of
Kuramoto oscillators can induce explosive synchronization (ES) in the
multiplexed layers. Along with the {\alpha} values, the hysteresis width is
determined by the interlayer coupling strength and the frequency mismatch
between the mirror (inter-connected) nodes. A mean-field analysis is performed
to support the numerical results. Similar to the earlier works, we find that
the suppression of synchronization is accountable for the origin of ES. The
robustness of ES against changes in the network topology and frequency
distribution is tested. Finally, taking a suggestion from the synchronized
state of the multiplex networks, we extend the results to the classical concept
of the single-layer networks in which some specific links are assigned a
phase-shifted coupling. Different methods have been introduced in the past
years to incite ES in coupled oscillators; our results indicate that a
phase-shifted coupling can also be one such method to achieve ES.Comment: 9 pages, 8 figure
Onset of Synchronization in Weighted Complex Networks: the Effect of Weight-Degree Correlation
By numerical simulations, we investigate the onset of synchronization of
networked phase oscillators under two different weighting schemes. In scheme-I,
the link weights are correlated to the product of the degrees of the connected
nodes, so this kind of networks is named as the weight-degree correlated (WDC)
network. In scheme-II, the link weights are randomly assigned to each link
regardless of the node degrees, so this kind of networks is named as the
weight-degree uncorrelated (WDU) network. Interestingly, it is found that by
increasing a parameter that governs the weight distribution, the onset of
synchronization in WDC network is monotonically enhanced, while in WDU network
there is a reverse in the synchronization performance. We investigate this
phenomenon from the viewpoint of gradient network, and explain the contrary
roles of coupling gradient on network synchronization: gradient promotes
synchronization in WDC network, while deteriorates synchronization in WDU
network. The findings highlight the fact that, besides the link weight, the
correlation between the weight and node degree is also important to the network
dynamics.Comment: 9 pages, 6 figure