Author
D. L. Valladares
Other affiliations: University of Navarra
Bio: D. L. Valladares is an academic researcher from National University of San Luis. The author has contributed to research in topics: Synchronization of chaos & Synchronization (computer science). The author has an hindex of 5, co-authored 7 publications receiving 2362 citations. Previous affiliations of D. L. Valladares include University of Navarra.
Papers
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TL;DR: Synchronization of chaos refers to a process where two chaotic systems adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy) as discussed by the authors.
2,266 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: A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered, able to extrapolate the subspace dimensions from the zero coupling limit, where the division of dimensions as per the algorithm is exact.
Abstract: A method for reconstructing dimensions of subspaces for weakly coupled dynamical systems is offered. The tool is able to extrapolate the subspace dimensions from the zero coupling limit, where the division of dimensions as per the algorithm is exact. Implementation of the proposed technique to multivariate data demonstrates its effectiveness in disentangling subspace dimensionalities also in the case of emergent synchronized motions, for both numerical and experimental systems.
63 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: It is shown that a full phase synchronized state cannot be constructed without at least partial correlation in the chaotic amplitudes.
Abstract: We discuss the emergence of a collective phase locked state in an open chain of N unidirectionally weakly coupled nonidentical chaotic oscillators. Such a regime is characterized by a Lyapunov spectrum where $N\ensuremath{-}1$ exponents that were zero in the uncoupled regime assume negative values as the coupling strength increases. The dynamics of such collective state is studied, and a comparison is drawn with the case of phase synchronization of a pair of coupled chaotic oscillators. In particular, it is shown that a full phase synchronized state cannot be constructed without at least partial correlation in the chaotic amplitudes.
10 citations
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TL;DR: The major concepts and results recently achieved in the study of the structure and dynamics of complex networks are reviewed, and the relevant applications of these ideas in many different disciplines are summarized, ranging from nonlinear science to biology, from statistical mechanics to medicine and engineering.
9,441 citations
TL;DR: In this paper, the authors describe the rules of the ring, the ring population, and the need to get off the ring in order to measure the movement of a cyclic clock.
Abstract: 1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects
3,424 citations
TL;DR: The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research, and detail the analysis of data and indicate possible difficulties and pitfalls.
2,993 citations
TL;DR: This work offers a comprehensive review on both structural and dynamical organization of graphs made of diverse relationships (layers) between its constituents, and cover several relevant issues, from a full redefinition of the basic structural measures, to understanding how the multilayer nature of the network affects processes and dynamics.
2,669 citations
TL;DR: Synchronization of chaos refers to a process where two chaotic systems adjust a given property of their motion to a common behavior due to a coupling or to a forcing (periodical or noisy) as discussed by the authors.
2,266 citations