From synchronization to Lyapunov exponents and back (Articolo in rivista)

Type
Label
  • From synchronization to Lyapunov exponents and back (Articolo in rivista) (literal)
Anno
  • 2006-01-01T00:00:00+01:00 (literal)
Alternative label
  • Politi A., Ginelli F., Yanchuk S., Maistrenko Y. (2006)
    From synchronization to Lyapunov exponents and back
    in Physica. D, Nonlinear phenomena (Print)
    (literal)
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  • Politi A., Ginelli F., Yanchuk S., Maistrenko Y. (literal)
Pagina inizio
  • 90 (literal)
Pagina fine
  • 101 (literal)
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  • 224 (literal)
Rivista
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  • fasc. (1-2). Elsevier. Dynamics on Complex Networks and Applications. (literal)
Note
  • ISI Web of Science (WOS) (literal)
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  • a) CNR - Istituto dei Sistemi Complessi, Via Madonna del Piano, 10, I-50019 Sesto Fiorentino, Italy b) CEA–Service de Physique de l’Etat Condensé, Centre d’Etudes de Saclay, 91191 Gif-sur-Yvette, France c) Institute of Mathematics, National Academy of Sciences of Ukraine, 01601 Kyiv, Ukraine d) Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany e) Institute of Mathematics, Humboldt University of Berlin, Unter den Linden 6, 10099 Berlin, Germany f) Institute of Medicine and Virtual Institute of Neuromodulation, Research Centre Jülich, 52425 Jülich, Germany (literal)
Titolo
  • From synchronization to Lyapunov exponents and back (literal)
Abstract
  • The goal of this paper is twofold. In the first part we discuss a general approach to determine Lyapunov exponents from ensemble rather than time averages. The approach passes through the identification of locally stable and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy with generalized synchronization. The method is then applied to a periodically forced chaotic oscillator to show that the modulus of the Lyapunov exponent associated to the phase dynamics increases quadratically with the coupling strength and it is therefore different from zero already below the onset of phase synchronization. The analytical calculations are carried out for a model, the generalized special flow, that we construct as a simplified version of the periodically forced Rössler oscillator. (literal)
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