Resonant forcing of chaotic dynamics

Vadas Gintautas, Glenn Foster, Alfred W. Hübler

Research output: Contribution to journalArticlepeer-review

Abstract

We study resonances of multidimensional chaotic map dynamics. We use the calculus of variations to determine the additive forcing function that induces the largest response, that is, the greatest deviation from the unperturbed dynamics. We include the additional constraint that only select degrees of freedom be forced, corresponding to a very general class of problems in which not all of the degrees of freedom in an experimental system are accessible to forcing. We find that certain Lagrange multipliers take on a fundamental physical role as the efficiency of the forcing function and the effective forcing experienced by the degrees of freedom which are not forced directly. Furthermore, we find that the product of the displacement of nearby trajectories and the effective total forcing function is a conserved quantity. We demonstrate the efficacy of this methodology with several examples.

Original languageEnglish (US)
Pages (from-to)617-629
Number of pages13
JournalJournal of Statistical Physics
Volume130
Issue number3
DOIs
StatePublished - Feb 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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