297 research outputs found
Explosive synchronization in weighted complex networks
The emergence of dynamical abrupt transitions in the macroscopic state of a
system is currently a subject of the utmost interest. Given a set of phase
oscillators networking with a generic wiring of connections and displaying a
generic frequency distribution, we show how combining dynamical local
information on frequency mismatches and global information on the graph
topology suggests a judicious and yet practical weighting procedure which is
able to induce and enhance explosive, irreversible, transitions to
synchronization. We report extensive numerical and analytical evidence of the
validity and scalability of such a procedure for different initial frequency
distributions, for both homogeneous and heterogeneous networks, as well as for
both linear and non linear weighting functions. We furthermore report on the
possibility of parametrically controlling the width and extent of the
hysteretic region of coexistence of the unsynchronized and synchronized states
The interplay of university and industry through the FP5 network
To improve the quality of life in a modern society it is essential to reduce
the distance between basic research and applications, whose crucial roles in
shaping today's society prompt us to seek their understanding. Existing studies
on this subject, however, have neglected the network character of the
interaction between university and industry. Here we use state-of-the-art
network theory methods to analyze this interplay in the so-called Framework
Programme--an initiative which sets out the priorities for the European Union's
research and technological development. In particular we study in the 5th
Framework Programme (FP5) the role played by companies and scientific
institutions and how they contribute to enhance the relationship between
research and industry. Our approach provides quantitative evidence that while
firms are size hierarchically organized, universities and research
organizations keep the network from falling into pieces, paving the way for an
effective knowledge transfer.Comment: 21 pages (including Appendix), 8 figures. Published online at
http://stacks.iop.org/1367-2630/9/18
Unveiling the connectivity of complex networks using ordinal transition methods
Ordinal measures provide a valuable collection of tools for analyzing
correlated data series. However, using these methods to understand the
information interchange in networks of dynamical systems, and uncover the
interplay between dynamics and structure during the synchronization process,
remains relatively unexplored. Here, we compare the ordinal permutation
entropy, a standard complexity measure in the literature, and the permutation
entropy of the ordinal transition probability matrix that describes the
transitions between the ordinal patterns derived from a time series. We find
that the permutation entropy based on the ordinal transition matrix outperforms
the rest of the tested measures in discriminating the topological role of
networked chaotic R\"ossler systems. Since the method is based on permutation
entropy measures, it can be applied to arbitrary real-world time series
exhibiting correlations originating from an existing underlying unknown network
structure. In particular, we show the effectiveness of our method using
experimental datasets of networks of nonlinear oscillators.Comment: 9 pages, 5 figure
Deterministic and stochastic cooperation transitions in evolutionary games on networks
Although the cooperative dynamics emerging from a network of interacting
players has been exhaustively investigated, it is not yet fully understood when
and how network reciprocity drives cooperation transitions. In this work, we
investigate the critical behavior of evolutionary social dilemmas on structured
populations by using the framework of master equations and Monte Carlo
simulations. The developed theory describes the existence of absorbing,
quasi-absorbing, and mixed strategy states and the transition nature,
continuous or discontinuous, between the states as the parameters of the system
change. In particular, when the decision-making process is deterministic, in
the limit of zero effective temperature of the Fermi function, we find that the
copying probabilities are discontinuous functions of the system's parameters
and of the network degrees sequence. This may induce abrupt changes in the
final state for any system size, in excellent agreement with the Monte Carlo
simulation results. Our analysis also reveals the existence of continuous and
discontinuous phase transitions for large systems as the temperature increases,
which is explained in the mean-field approximation. Interestingly, for some
game parameters, we find optimal "social temperatures" maximizing/minimizing
the cooperation frequency/density.Comment: 14 pages, 5 figure
Synchronization interfaces and overlapping communities in complex networks
We show that a complex network of phase oscillators may display interfaces
between domains (clusters) of synchronized oscillations. The emergence and
dynamics of these interfaces are studied in the general framework of
interacting phase oscillators composed of either dynamical domains (influenced
by different forcing processes), or structural domains (modular networks). The
obtained results allow to give a functional definition of overlapping
structures in modular networks, and suggest a practical method to identify
them. As a result, our algorithm could detect information on both single
overlapping nodes and overlapping clusters.Comment: 5 pages, 4 figure
Dynamical and spectral properties of complex networks
Dynamical properties of complex networks are related to the spectral
properties of the Laplacian matrix that describes the pattern of connectivity
of the network. In particular we compute the synchronization time for different
types of networks and different dynamics. We show that the main dependence of
the synchronization time is on the smallest nonzero eigenvalue of the Laplacian
matrix, in contrast to other proposals in terms of the spectrum of the
adjacency matrix. Then, this topological property becomes the most relevant for
the dynamics.Comment: 14 pages, 5 figures, to be published in New Journal of Physic
Nonlocal analysis of modular roles
We introduce a new methodology to characterize the role that a given node plays inside the community structure of a complex network. Our method relies on the ability of the links to reduce the number of steps between two nodes in the network, which is measured by the number of shortest paths crossing each link, and its impact on the node proximity. In this way, we use node closeness to quantify the importance of a node inside its community. At the same time, we define a participation coefficient that depends on the shortest paths contained in the links that connect two communities. The combination of both parameters allows to identify the role played by the nodes in the network, following the same guidelines introduced by Guimerà et al. [Guimerà & Amaral, 2005] but, in this case, considering global information about the network. Finally, we give some examples of the hub characterization in real networks and compare our results with the parameters most used in the literature
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