Showing papers by "Stefano Boccaletti published in 2000"
TL;DR: In this paper, the Ott-Grebogi-Yorke (OGY) method and the adaptive method for chaotic control are discussed. But the authors focus on the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions.
742 citations
TL;DR: Intermittent lag synchronization of two nonidentical symmetrically coupled Rossler systems is investigated, wherein the intermittent bursts away from the lag synchronization regime correspond to jumps of the system toward other lag configurations.
Abstract: Intermittent lag synchronization of two nonidentical symmetrically coupled Rossler systems is investigated. This phenomenon can be seen as a process wherein the intermittent bursts away from the lag synchronization regime correspond to jumps of the system toward other lag configurations. During these jumps, the chaotic trajectory visits closely a periodic orbit. The identification of the different lag configurations and the measure of the fraction of time passed by the system in each one of them provide information on the global scenario of transitions undergone by the system before reaching perfect lag synchronization.
148 citations
TL;DR: In this paper, the morphology of the spatial structures displayed by an optical system consisting of a liquid crystal light valve (LCLV) in a feedback configuration, as the feedback is gradually tuned from purely diffractive to mixed interferential and diffractive.
Abstract: We compare the morphology of the spatial structures displayed by an optical system consisting of a liquid crystal light valve (LCLV) in a feedback configuration, as the feedback is gradually tuned from purely diffractive to mixed interferential and diffractive. Different kinds of spatially coherent structures (e.g. hexagons, rolls), as well as localized structures and space-time turbulent patterns are observed. The features of the localized structures change with the parameter setting, and certain regions of the parameter space provide stable clusters of isolated spots (`molecules'). Numerical simulations based on a Kerr-like model of the LCLV are in agreement with the experimental observations. We analyse the links between the observed behaviours and the results of a linear-stability analysis of the underlying homogeneous stationary states.
51 citations
TL;DR: The creation of a lower dimensional chaotic state is described, showing that it is associated with an abrupt transition in the Lyapunov spectrum, and the robustness of this state against noise is discussed.
Abstract: Synchronization features are explored for a pair of chaotic high-dimensional bidirectionally coupled structurally nonequivalent systems. We find two regimes of synchronization in dependence on the coupling strength: creation of a lower dimensional chaotic state, and for larger coupling a transition toward a stable periodic motion. We characterize this new state, showing that it is associated with an abrupt transition in the Lyapunov spectrum. The robustness of this state against noise is discussed, and the use of this dynamical property as a possible approach for the control of chaos is outlined.
44 citations
TL;DR: Experimental evidence of phase synchronization of high dimensional chaotic oscillators in a laboratory experiment that consists of a thermocapillary driven convective cell in a time dependent chaotic regime is reported.
Abstract: We report experimental evidence of phase synchronization of high dimensional chaotic oscillators in a laboratory experiment. The experiment consists of a thermocapillary driven convective cell in a time dependent chaotic regime. The synchronized states emerge as a consequence of a localized temperature perturbation to the heater. The transition to phase synchronization is studied as a function of the external perturbations. The existence and stability conditions for this phenomenon are discussed.
41 citations
TL;DR: A nonlinear optical system consisting of a liquid crystal light valve with feedback can display an enormous variety of spatial patterns starting from the basic principles of operation, and several physical configurations enlighting the specificity of each one and the mechanism by which it leads to certain rules of pattern selection as discussed by the authors.
Abstract: A nonlinear optical system, consisting of a liquid crystal light valve with feedback, can display an enormous variety of spatial patterns Starting from the basic principles of operation, we review several physical configurations enlighting the specificity of each one and the mechanism by which it leads to certain rules of pattern selection
28 citations
TL;DR: This work characterize the synchronization of two nonidentical spatially extended fields ruled by one-dimensional Complex Ginzburg–Landau equations, in the two regimes of phase and amplitude turbulence.
Abstract: We characterize the synchronization of two nonidentical spatially extended fields ruled by one-dimensional Complex Ginzburg–Landau equations, in the two regimes of phase and amplitude turbulence. If two fields display the same dynamical regime, the coupling induces a transition to a completely synchronized state. When, instead, the two fields are in different dynamical regimes, the transition to complete synchronization is mediated by defect synchronization. In the former case, the synchronized manifold is dynamically equivalent to that of the unsynchronized systems, while in the latter case the synchronized state substantially differs from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects.
14 citations
TL;DR: It is shown that, in the limit of three controllers per correlation length, the synchronization behavior is not affected if the product varepsilonN(c)/N is kept constant, providing a sort of integral behavior for localized synchronization.
Abstract: We report the synchronization of two nonidentical spatially extended fields, ruled by one-dimensional complex Ginzburg-Landau equations. The two fields are prepared in different dynamical regimes, and interact via an imperfect coupling consisting of a given number of local controllers ${N}_{c}.$ The strength of the coupling is ruled by the parameter $\ensuremath{\varepsilon}.$ We show that, in the limit of three controllers per correlation length, the synchronization behavior is not affected if the product $\ensuremath{\varepsilon}{N}_{c}/N$ is kept constant, providing a sort of integral behavior for localized synchronization.
13 citations
TL;DR: The emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean field interaction, is described, showing that the resulting behavior cooperatively maximizes the energy of the mean field activity.
Abstract: We describe the emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean field interaction. This kind of interaction is responsible for the appearence of a collective state, wherein the mean field evolution of each lattice undergoes a periodic behavior in space. We analyze the transition to such a state in an ensemble of one-dimensional lattices of logistic maps, showing that the resulting behavior cooperatively maximizes the energy of the mean field activity.
6 citations
TL;DR: Two-dimensional extended bistable systems with drift after a quench above threshold are analyzed and can be separated into successive stages: linear growth and diffusion, coarsening, and transport, leading finally to a quasi-one-dimensional kink-antikink state.
Abstract: Motivated by experiments on optical patterns we analyze two-dimensional extended bistable systems with drift after a quench above threshold. The evolution can be separated into successive stages: linear growth and diffusion, coarsening, and transport, leading finally to a quasi-one-dimensional kink-antikink state. The phenomenon is general and occurs when the bistability relates to uniform phases or two different patterns.
3 citations
TL;DR: In this paper, a numerical model, derived from the Maxwell-Bloch equations and including symmetry breaking terms, enables the interpretation of the main experimental features in an annular CO2 laser.
Abstract: Competition among modes in an annular CO2 laser has been experimentally and numerically analyzed. During the coexistence of different patterns, each of them resulting from the interaction of two transverse modes with opposite angular momentum, chaos has been experimentally detected. A numerical model, derived from the Maxwell-Bloch equations and including symmetry breaking terms, enables the interpretation of the main experimental features.
01 Jan 2000
TL;DR: It is likely that this difficulty in defining the “measured system” and the large time variability of the Signal to Noise Ratio (SNR) is one of the reasons for the wide spectrum of results that can be found in the literature on chaotic estimators especially when investigating spontaneous activity.
Abstract: Spontaneous activity of the human brain in normal subjects is not likely to be “low dimensional” being the result of superpositions of many correlated and uncorrelated activities These activities are not constantly present, neither detectable uniformly over the whole scalp It is likely that this difficulty in defining the “measured system” and the large time variability of the Signal to Noise Ratio (SNR) is one of the reasons for the wide spectrum of results that can be found in the literature on chaotic estimators especially when investigating spontaneous activity As an example the Correlation Dimension (CD) for the waking stage (mostly α rhythm) ranges from 24 to 11 (see, for example, [1]) While some agreement can be found on the dimension decrease under epileptic seizures or other specific pathologies the attempts for a dimensional classification of α rhythm have been mostly unsuccessful