Resonances of nonlinear oscillators

Christoph Wargitsch, Alfred Hübler

Research output: Contribution to journalArticlepeer-review


We show that nonlinear oscillators have a large response to special aperiodic driving forces. If these forces are selected to minimize the driving effort for a given terminal energy, these forces are given by the time-reflected transient of the unperturbed dynamics (the ''principle of the dynamical key''). We provide a proof of this principle. We find that these optimal forcing functions have very similar dynamics for several different norms. We present a quantitative comparison of the energy transfer for sinusoidal and optimal driving forces. We find that aperiodic driving forces are most effective for large nonlinearity and small friction. We show that this optimal control is stable for several important systems.

Original languageEnglish (US)
Pages (from-to)1508-1519
Number of pages12
JournalPhysical Review E
Issue number2
StatePublished - 1995
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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