Showing papers by "Stefano Boccaletti published in 2007"

Detecting complex network modularity by dynamical clustering

Abstract: Based on cluster desynchronization properties of phase oscillators, we introduce an efficient method for the detection and identification of modules in complex networks. The performance of the algorithm is tested on computer generated and real-world networks whose modular structure is already known or has been studied by means of other methods. The algorithm attains a high level of precision, especially when the modular units are very mixed and hardly detectable by the other methods, with a computational effort O(KN) on a generic graph with N nodes and K links.

Multiscale vulnerability of complex networks

Abstract: We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links’ betweenness. We show that the proposed approach is able to properly describe some cases for which earlier measures of vulnerability fail. The relevant applications of our method for technological network design are outlined.

Identification of network modules by optimization of ratio association.

Abstract: We introduce a novel method for identifying the modular structures of a network based on the maximization of an objective function: the ratio association. This cost function arises when the communities detection problem is described in the probabilistic autoencoder frame. An analogy with kernel k-means methods allows us to develop an efficient optimization algorithm, based on the deterministic annealing scheme. The performance of the proposed method is shown on real data sets and on simulated networks.

Synchronization properties of network motifs

Abstract: We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node subgraph, we propose an analytic method to measure the stability of the synchronous state (SSS) the subgraph displays. We show that, for undirected graphs, the SSS is correlated with the relative abundance, while in directed graphs the correlation exists only for some specific motifs.

Length distribution of laminar phases for type-I intermittency in the presence of noise.

Abstract: We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar phases, with the law for the mean length of the laminar phases versus the critical parameter deduced earlier [W.-H. Kye and C.-M. Kim, Phys. Rev. E 62, 6304 (2000)] being the corollary fact of the developed theory. We find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations. We discuss also how this mechanism is expected to take place in other relevant physical circumstances.

Chaos suppression through asymmetric coupling.

Abstract: We study pairs of identical coupled chaotic oscillators. In particular, we have used Roessler (in the funnel and no funnel regimes), Lorenz, and four-dimensional chaotic Lotka-Volterra models. In all four of these cases, a pair of identical oscillators is asymmetrically coupled. The main result of the numerical simulations is that in all cases, specific values of coupling strength and asymmetry exist that render the two oscillators periodic and synchronized. The values of the coupling strength for which this phenomenon occurs is well below the previously known value for complete synchronization. We have found that this behavior exists for all the chaotic oscillators that we have used in the analysis. We postulate that this behavior is presumably generic to all chaotic oscillators. In order to complete the study, we have tested the robustness of this phenomenon of chaos suppression versus the addition of some Gaussian noise. We found that chaos suppression is robust for the addition of finite noise level. Finally, we propose some extension to this research.

The complex network of musical tastes

Abstract: We present an empirical study of the evolution of a social network constructed under the influence of musical tastes. The network is obtained thanks to the selfless effort of a broad community of users who share playlists of their favourite songs with other users. When two songs co-occur in a playlist a link is created between them, leading to a complex network where songs are the fundamental nodes. In this representation, songs in the same playlist could belong to different musical genres, but they are prone to be linked by a certain musical taste (e.g. if songs A and B co-occur in several playlists, an user who likes A will probably like also B). Indeed, playlist collections such as the one under study are the basic material that feeds some commercial music recommendation engines. Since playlists have an input date, we are able to evaluate the topology of this particular complex network from scratch, observing how its characteristic parameters evolve in time. We compare our results with those obtained from an artificial network defined by means of a null model. This comparison yields some insight on the evolution and structure of such a network, which could be used as ground data for the development of proper models. Finally, we gather information that can be useful for the development of music recommendation engines and give some hints about how top-hits appear.

The birth of defects in pattern formation: testing of the Kibble-Zurek mechanism

Abstract: The extension of the cosmological mechanism of Kibble to second order phase transitions in condensed matter systems by Zurek, can be further generalized to bifurcations of out-of-equilibrium systems in continuum media, since the argument used in the derivation of the Kibble–Zurek scaling law is general. Here we review the validity of such scaling comparing several bifurcations where the test has been checked. Also, new experimental results of a nonlinear optical system are reported.

Detecting and localizing the foci in human epileptic seizures

Abstract: We consider the electrical signals recorded from a subdural array of electrodes placed on the pial surface of the brain for chronic evaluation of epileptic patients before surgical resection. A simple and computationally fast method to analyze the interictal phase synchrony between such electrodes is introduced and developed with the aim of detecting and localizing the foci of the epileptic seizures. We evaluate the method by comparing the results of surgery to the localization predicted here. We find an indication of good correspondence between the success or failure in the surgery and the agreement between our identification and the regions actually operated on.

Growing hierarchical scale-free networks by means of nonhierarchical processes

Abstract: We introduce a fully nonhierarchical network growing mechanism, that furthermore does not impose explicit preferential attachment rules. The growing procedure produces a graph featuring power-law degree and clustering distributions, and manifesting slightly disassortative degree-degree correlations. The rigorous rate equations for the evolution of the degree distribution and for the conditional degree-degree probability are derived.

Synchronization processes in complex networks

Abstract: During the last decades the emergence of collective dynamics in large networks of coupled units has been investigated in fields such as optics, chemistry, biology and ecology. Recently, complex networks have provided a challenging framework for the study of synchronization of dynamical units, based on the interplay between complexity in the overall topology and local dynamical properties of the coupled units. In this work, we review the constructive role played by such complex wirings for the synchronization of networks of coupled dynamical systems. We review the main techniques that have been proposed for assessing the propensity for synchronization (synchronizability) of a given networked system. We will also describe the main applications, especially in the view of selecting the optimal topology in the coupling configuration that provides enhancement of the synchronization features.

Pinning control of spatiotemporal chaos in the LCLV device.

Abstract: We study the feasibility of transferring data in an optical device by using a limited number of parallel channels. By applying a spatially localized correcting term to the evolution of a liquid crystal light valve in its spatio--temporal chaotic regime, we are able to restore the dynamics to a specified target pattern. The system is controlled in a finite time. The number and position of pinning points needed to attain control is also investigated.

Modules identification by a Dynamical Clustering algorithm based on chaotic Rössler oscillators

Abstract: A new dynamical clustering algorithm for the identification of modules in complex networks has been recently introduced [1]. In this paper we present a modified version of this algorithm based on a system of chaotic Rossler oscillators and we test its sensitivity on real and computer generated networks with a well known modular structure.

Modules identification by a Dynamical Clustering algorithm based on chaotic R\"ossler oscillators

Abstract: A new dynamical clustering algorithm for the identification of modules in complex networks has been recently introduced \cite{BILPR}. In this paper we present a modified version of this algorithm based on a system of chaotic Roessler oscillators and we test its sensitivity on real and computer generated networks with a well known modular structure.

Automatic control and tracking of periodic orbits in chaotic systems.

Abstract: Based on an automatic feedback adjustment of an additional parameter of a dynamical system, we propose a strategy for controlling periodic orbits of desired periods in chaotic dynamics and tracking them toward the set of unstable periodic orbits embedded within the original chaotic attractor. The method does not require information on the system to be controlled, nor on any reference states for the targets, and it overcomes some of the difficulties encountered by other techniques. Assessments of the method's effectiveness and robustness are given by means of the application of the technique to the stabilization of unstable periodic orbits in both discrete- and continuous-time systems.

Coherence resonance in a fitzhugh–nagumo electronic system

Abstract: We investigate Coherence Resonance phenomenon in an electronic circuit obeying the FitzHugh–Nagumo dynamics. The phenomenon is induced with a noise source exhibiting different nature. The resonance behavior results are significantly reinforced when experimental parameters are tuned in order to place the stable fixed point closer to the excitability threshold of spiking behavior, as well as when the time scales of the circuit are properly modified.

Searching for modules of networks in the auto‐encoder frame

Abstract: We introduce a novel method for identifying the modular structures of a network: this problem is described as a process of compression of information, by means of the autoencoder frame. As a result, the best partition in modules is found to be the maximizer of an objective function: the ratio association. The performance of the proposed method is shown on a real data set and on simulated networks. The optimization algorithm we use is based on the deterministic annealing scheme.

Synchronization in Coupled and Free Chaotic Systems

Abstract: Global bifurcations in dynamical systems are of considerable interest because they can lead to the creation of chaotic behaviour [Hilborn, 1994]. Global bifurcations are to be distinguished from local bifurcations around an unstable periodic solution. Typically, they occur when a homoclinic point is created. A homoclinic point is an intersection point between the stable and the unstable manifold of a steady state saddle point p on the Poincare section of a, at least, 3D flow. The presence of a homoclinic point implies a complicated geometrical structure of both the stable and the unstable manifolds usally referred to as a homoclinic tangle. When a homoclinic tangle has developed, a trajfectory that comes close to the saddle point behaves in an erratic way, showing sensitivity to initial conditions.