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 language | English |
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Pages (from-to) | 5242-5252 |
Number of pages | 11 |
Journal | Physical Review E |
Volume | 59 |
Issue number | 5 |
DOIs | |
State | Published - 1999 |