73 research outputs found
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
Synchronization of mobile chaotic oscillator networks
We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents' states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks
Synchronization reveals topological scales in complex networks
We study the relationship between topological scales and dynamic time scales
in complex networks. The analysis is based on the full dynamics towards
synchronization of a system of coupled oscillators. In the synchronization
process, modular structures corresponding to well defined communities of nodes
emerge in different time scales, ordered in a hierarchical way. The analysis
also provides a useful connection between synchronization dynamics, complex
networks topology and spectral graph analysis.Comment: 4 pages, 3 figure
Detección de tormentas geomagnéticas
La investigación espacial a través del uso de dispositivos como los CubeSat se está abriendo camino a pasos cada vez más grandes, nuestra idea de proyecto busca sumarse a este campo, contribuyendo a un área en la que vemos una oportunidad de aporte de datos de crucial importancia. En este artÃculo les presentamos una forma innovadora de medir las tormentas geomagnéticas desde el espacio a bajo costo ocupando solo una bandeja estándar de Cubesat, el contexto que nos rodea, los requerimientos necesarios para un funcionamiento teórico, la tecnologÃa adquirida para la demostración experimental, y su implementación como carga útil secundaria en el USAT-I (Satélite Universitario de la Universidad Nacional de La Plata).Facultad de IngenierÃ
Spectral analysis of synchronization in mobile networks
We here analyze a system consisting of agents moving in a two-dimensional space that interact with other agents if they are within a finite range. Considering the motion and the interaction of the agents, the system can be understood as a network with a time-dependent topology. Dynamically, the agents are assumed to be identical oscillators, and the system will eventually reach a state of complete synchronization. In a previous work, we have shown that two qualitatively different mechanisms leading to synchronization in such mobile networks exist, namely global synchronization and local synchronization, depending on the parameters that characterize the oscillatory dynamics and the motion of the agents [1]. In this contribution we show that the spectral pattern differs between the two synchronization mechanisms. For global synchronization the spectrum is flat, which means that all eigenmodes contribute identically. For local synchronization, instead, the synchronization dynamics is determined mostly by the eigenmodes whose eigenvalues are close to zero. This result suggests that the global synchronization mechanism achieves fast synchronization by efficiently using the fast decaying eigenmodes (larger eigenvalues)
Efficiency of informational transfer in regular and complex networks
We analyze the process of informational exchange through complex networks by
measuring network efficiencies. Aiming to study non-clustered systems, we
propose a modification of this measure on the local level. We apply this method
to an extension of the class of small-worlds that includes {\it declustered}
networks, and show that they are locally quite efficient, although their
clustering coefficient is practically zero. Unweighted systems with small-world
and scale-free topologies are shown to be both globally and locally efficient.
Our method is also applied to characterize weighted networks. In particular we
examine the properties of underground transportation systems of Madrid and
Barcelona and reinterpret the results obtained for the Boston subway network.Comment: 10 pages and 9 figure
Spectral properties of the Laplacian of multiplex networks.
One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [ Phys. Rev. Lett. 110 028701 (2013)], some of the authors proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability
Comparing community structure identification
We compare recent approaches to community structure identification in terms
of sensitivity and computational cost. The recently proposed modularity measure
is revisited and the performance of the methods as applied to ad hoc networks
with known community structure, is compared. We find that the most accurate
methods tend to be more computationally expensive, and that both aspects need
to be considered when choosing a method for practical purposes. The work is
intended as an introduction as well as a proposal for a standard benchmark test
of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as
appears in JSTA
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