5,870 research outputs found
Synchronization in complex networks
Synchronization processes in populations of locally interacting elements are
in the focus of intense research in physical, biological, chemical,
technological and social systems. The many efforts devoted to understand
synchronization phenomena in natural systems take now advantage of the recent
theory of complex networks. In this review, we report the advances in the
comprehension of synchronization phenomena when oscillating elements are
constrained to interact in a complex network topology. We also overview the new
emergent features coming out from the interplay between the structure and the
function of the underlying pattern of connections. Extensive numerical work as
well as analytical approaches to the problem are presented. Finally, we review
several applications of synchronization in complex networks to different
disciplines: biological systems and neuroscience, engineering and computer
science, and economy and social sciences.Comment: Final version published in Physics Reports. More information
available at http://synchronets.googlepages.com
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
Spatiotemporal Regularity in Networks with Stochastically Varying Links
In this work we investigate time varying networks with complex dynamics at
the nodes. We consider two scenarios of network change in an interval of time:
first, we have the case where each link can change with probability pt, i.e.
the network changes occur locally and independently at each node. Secondly we
consider the case where the entire connectivity matrix changes with probability
pt, i.e. the change is global. We show that network changes, occurring both
locally and globally, yield an enhanced range of synchronization. When the
connections are changed slowly (i.e. pt is low) the nodes display nearly
synchronized intervals interrupted by intermittent unsynchronized chaotic
bursts. However when the connections are switched quickly (i.e. pt is large),
the intermittent behavior quickly settles down to a steady synchronized state.
Furthermore we find that the mean time taken to reach synchronization from
generic random initial states is significantly reduced when the underlying
links change more rapidly. We also analyze the probabilistic dynamics of the
system with changing connectivity and the stable synchronized range thus
obtained is in broad agreement with those observed numerically.Comment: 15 pages, 8 figures, Keywords: Complex Networks, Temporal Networks,
Synchronization, Coupled Map Lattic
Universality in the synchronization of weighted random networks
Realistic networks display not only a complex topological structure, but also
a heterogeneous distribution of weights in the connection strengths. Here we
study synchronization in weighted complex networks and show that the
synchronizability of random networks with large minimum degree is determined by
two leading parameters: the mean degree and the heterogeneity of the
distribution of node's intensity, where the intensity of a node, defined as the
total strength of input connections, is a natural combination of topology and
weights. Our results provide a possibility for the control of synchronization
in complex networks by the manipulation of few parameters.Comment: 4 pages, 3 figure
Brain modularity controls the critical behavior of spontaneous activity
The human brain exhibits a complex structure made of scale-free highly
connected modules loosely interconnected by weaker links to form a small-world
network. These features appear in healthy patients whereas neurological
diseases often modify this structure. An important open question concerns the
role of brain modularity in sustaining the critical behaviour of spontaneous
activity. Here we analyse the neuronal activity of a model, successful in
reproducing on non-modular networks the scaling behaviour observed in
experimental data, on a modular network implementing the main statistical
features measured in human brain. We show that on a modular network, regardless
the strength of the synaptic connections or the modular size and number,
activity is never fully scale-free. Neuronal avalanches can invade different
modules which results in an activity depression, hindering further avalanche
propagation. Critical behaviour is solely recovered if inter-module connections
are added, modifying the modular into a more random structure.Comment: 5 pages, 6 figure
Breathing synchronization in interconnected networks
Global synchronization in a complex network of oscillators emerges from the
interplay between its topology and the dynamics of the pairwise interactions
among its numerous components. When oscillators are spatially separated,
however, a time delay appears in the interaction which might obstruct
synchronization. Here we study the synchronization properties of interconnected
networks of oscillators with a time delay between networks and analyze the
dynamics as a function of the couplings and communication lag. We discover a
new breathing synchronization regime, where two groups appear in each network
synchronized at different frequencies. Each group has a counterpart in the
opposite network, one group is in phase and the other in anti-phase with their
counterpart. For strong couplings, instead, networks are internally
synchronized but a phase shift between them might occur. The implications of
our findings on several socio-technical and biological systems are discussed.Comment: 7 pages, 3 figures + 3 pages of Supplemental Materia
Rhythmic inhibition allows neural networks to search for maximally consistent states
Gamma-band rhythmic inhibition is a ubiquitous phenomenon in neural circuits
yet its computational role still remains elusive. We show that a model of
Gamma-band rhythmic inhibition allows networks of coupled cortical circuit
motifs to search for network configurations that best reconcile external inputs
with an internal consistency model encoded in the network connectivity. We show
that Hebbian plasticity allows the networks to learn the consistency model by
example. The search dynamics driven by rhythmic inhibition enable the described
networks to solve difficult constraint satisfaction problems without making
assumptions about the form of stochastic fluctuations in the network. We show
that the search dynamics are well approximated by a stochastic sampling
process. We use the described networks to reproduce perceptual multi-stability
phenomena with switching times that are a good match to experimental data and
show that they provide a general neural framework which can be used to model
other 'perceptual inference' phenomena
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