Double autoresonance in two-dimensional dynamical systems

U. Rokni, L. Friedland

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The phenomenon of double autoresonance in dynamical systems with two degrees of freedom is examined. We analyze the motion of a particle in a two-dimensional centrally symmetric potential, subject to a homogeneous quasiperiodic external field of elliptical polarization. It is shown that if the particle has a sufficiently small initial energy, a double resonance is established when the slowly varying driving frequency approaches the linear resonance frequency. As the driving frequency is changed further, the double resonance is maintained, causing a continuous excitation of the oscillator. When nonlinearity becomes significant, the motion transforms into nearly circular oscillations. The necessary conditions for the persistence of the autoresonance are studied in detail.

Original languageEnglish
Pages (from-to)5242-5252
Number of pages11
JournalPhysical Review E
Volume59
Issue number5
DOIs
StatePublished - 1999

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