Showing papers by "Stefano Boccaletti published in 2008"

Synchronization of moving chaotic agents.

Abstract: We consider a set of mobile agents in a two dimensional space, each one of them carrying a chaotic oscillator, and discuss the related synchronization issues under the framework of time-variant networks. In particular, we show that, as far as the time scale for the motion of the agents is much shorter than that of the associated dynamical systems, the global behavior can be characterized by a scaled all-to-all Laplacian matrix, and the synchronization conditions depend on the agent density on the plane.

Synchronization interfaces and overlapping communities in complex networks.

Abstract: 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 for graphs composed of either dynamical domains (influenced by different forcing processes), or structural domains (modular networks). The obtained results allow us to give a functional definition of overlapping structures in modular networks, and suggest a practical method able to give information on overlapping clusters in both artificially constructed and real world modular networks.

The Synchronized Dynamics of Complex Systems

Abstract: Publisher Summary This chapter presents the case of two coupled identical systems. The chapter describes the first historical studies on complete synchronization (CS) phenomena of coupled chaotic systems, both for low and for high dimensional situations, and discusses the relevant problem of assessing the stability conditions for the synchronization manifold. The chapter discusses the case of nonidentical systems and summarizes the novel synchronization regimes that arise in this context. The chapter focuses on the transitional behaviors from nonsynchronized to synchronized states. It describes a situation that is frequently encountered in real system. The chapter discusses the case of distributed and extended systems. The chapter presents the description of large ensembles of chaotic units and provides an overview of synchronization effects in coupled continuous space-extended systems. The chapter also describes the synchronization processes emerging in complex networks of dynamical units.

Phase locking induces scale-free topologies in networks of coupled oscillators.

Abstract: An initial unsynchronized ensemble of networking phase oscillators is further subjected to a growing process where a set of forcing oscillators, each one of them following the dynamics of a frequency pacemaker, are added to the pristine graph. Linking rules based on dynamical criteria are followed in the attachment process to force phase locking of the network with the external pacemaker. We show that the eventual locking occurs in correspondence to the arousal of a scale-free degree distribution in the original graph.

Synchronization in networks of slightly nonidentical elements

Abstract: We study synchronization processes in networks of slightly nonidentical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in parameters can be properly modeled by a noise term affecting the stability of the synchronous invariant solution emerging for identical systems when the parameter is set at the mean value of the original distribution.

Synchronization in networks of spatially extended systems.

Abstract: Synchronization processes in networks of spatially extended dynamical systems are analytically and numerically studied. We focus on the relevant case of networks whose elements (or nodes) are spatially extended dynamical systems, with the nodes being connected with each other by scalar signals. The stability of the synchronous spatio-temporal state for a generic network is analytically assessed by means of an extension of the master stability function approach. We find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations. The efficiency and reliability of this method is illustrated numerically with networks of beam-plasma chaotic systems (Pierce diodes). We discuss also how the revealed regularities are expected to take place in other relevant physical and biological circumstances.

Disorder and decision cost in spatial networks.

Abstract: We introduce the concept of decision cost of a spatial graph, which measures the disorder of a given network taking into account not only the connections between nodes but their position in a two-dimensional map. The influence of the network size is evaluated and we show that normalization of the decision cost allows us to compare the degree of disorder of networks of different sizes. Under this framework, we measure the disorder of the connections between airports of two different countries and obtain some conclusions about which of them is more disordered. The introduced concepts (decision cost and disorder of spatial networks) can easily be extended to Euclidean networks of higher dimensions, and also to networks whose nodes have a certain fitness property (i.e., one-dimensional).

Attractor selection in a modulated laser and in the Lorenz circuit

Abstract: By tuning a control parameter, a chaotic system can either display two or more attractors (generalized multistability) or exhibit an interior crisis, whereby a chaotic attractor suddenly expands to include the region of an unstable orbit (bursting regime). Recently, control of multistability and bursting have been experimentally proved in a modulated class B laser by means of a feedback method. In a bistable regime, the method relies on the knowledge of the frequency components of the two attractors. Near an interior crisis, the method requires retrieval of the unstable orbit colliding with the chaotic attractor. We also show that a suitable parameter modulation is able to control bistability in the Lorenz system. We observe that, for every given modulation frequency, the chaotic attractor is destroyed under a boundary crisis. The threshold control amplitude depends on the control frequency and the location of the operating point in the bistable regime. Beyond the boundary crisis, the system remains in the steady state even if the control is switched off, demonstrating control of bistability.

Synchronization in network of pierce diodes

Abstract: We report results on synchronization processes in complex networks of spatially extended chaotic systems. The method of the analysis of the stability of the network synchronous spatio-temporal state has been developed. The technique both for the stability analysis of the synchronous state in such systems and for the spatial master stability function calculation has been developed. The efficiency of the proposed approach has been illustrated by the consideration of the complex network of beam-plasma chaotic systems (Pierce diodes).

Pinning control of spatio temporal chaos in nonlinear optics

Abstract: We have studied numerically the influence of the number of controllers in the control of a spatial pattern in an optical device. In this article, we focus on the liquid crystal light valve (LCLV) which is known to exhibit spatio-temporal chaotic states in some range of parameters. By applying a correcting term in the intensity proportional to the difference between the light intensity of the target pattern and the chaos state, the system is driven to the target pattern in finite time. In addition, we study the number of pinning points and their positions to reach the control of the pattern.