Characterizing the Response of Chaotic Systems

Giovanni Giacomelli, Stephane Barland, Massimo Giudici, Antonio Politi

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We characterize the response of a chaotic system by investigating ensembles of, rather than single, trajectories. Time-periodic stimulations are experimentally and numerically investigated. This approach allows detecting and characterizing a broad class of coherent phenomena that go beyond generalized and phase synchronization. In particular, we find that a large average response is not necessarily related to the presence of standard forms of synchronization. Moreover, we study the stability of the response, by introducing an effective method to determine the largest nonzero eigenvalue -¿1 of the corresponding Liouville-type operator, without the need of directly simulating it. The exponent ¿1 is a dynamical invariant, which complements the standard characterization provided by the Lyapunov exponents.

Original languageEnglish
Article number194101
Number of pages4
JournalPhysical Review Letters
Issue number19
Early online date10 May 2010
Publication statusPublished - 14 May 2010


  • statistical-mechanics
  • large numbers
  • dynamics
  • ensembles
  • law


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