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In a spirit akin to the sandpile model of self-organized criticality, we present a simple statistical model of the cellular-automaton type which simulates the role of an asperity in the dynamics of a one-dimensional fault. This model produces an earthquake spectrum similar to the characteristic-earthquake behaviour of some seismic faults. This model, that(More)
We derive the mean-field equations characterizing the dynamics of a rumor process that takes place on top of complex heterogeneous networks. These equations are solved numerically by means of a stochastic approach. First, we present analytical and Monte Carlo calculations for homogeneous networks and compare the results with those obtained by the numerical(More)
– In this work, we study the synchronization of coupled phase oscillators on the underlying topology of scale-free networks. In particular, we assume that each network's component is an oscillator and that each interacts with the others following the Kuramoto model. We then study the onset of global phase synchronization and fully characterize the system's(More)
We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field-like rate equations describing the system and allows us to work with very large system sizes, where Monte Carlo simulations are useless due to memory needs. We then study the susceptible-infected-removed(More)
– The instability introduced in a large scale-free network by the triggering of node-breaking avalanches is analyzed using the fiber-bundle model as conceptual framework. We found, by measuring the size of the giant component, the avalanche size distribution and other quantities, the existence of an abrupt transition. This test of strength for complex(More)
A network with local dynamics of logistic type is considered. We implement a mean-field multiplicative coupling among first-neighbor nodes. When the coupling parameter is small the dynamics is dissipated and there is no activity: the network is turned off. For a critical value of the coupling a non-null stable synchronized state, which represents a turned(More)
Using the global fiber bundle model as a tractable scheme of progressive fracture in heterogeneous materials, we define the branching ratio in avalanches as a suitable order parameter to clarify the order of the phase transition occurring at the collapse of the system. The model is analyzed using a probabilistic approach suited to smooth fluctuations. The(More)
The recently introduced Minimalist Model [Vázquez-Prada et al, 2002] of characteristic earthquakes provides a simple representation of the seismicity originated in a single fault. Here, we first characterize the properties of this model for large systems. Then, assuming, as it has been observed, that the size of the faults in a big enough region is(More)
The dynamics of a fibre-bundle type model with equal load sharing rule is numerically studied. The system, formed by N elements, is driven by a slow increase of the load upon it which is removed in a novel way through internal transfers to the elements broken during avalanches. When an avalanche ends, failed elements are regenerated with strengths taken(More)
The time to failure, T, of dynamical models of fracture for a hierarchical load-transfer geometry is studied. Using a probabilistic strategy and juxtaposing hierarchical structures of height n, we devise an exact method to compute T, for structures of height n+1. Bounding T, for large n, we are able to deduce that the time to failure tends to a nonzero(More)