Nonperiodic driving of coupled oscillators: a spherical swing
Abstract
Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one oscillator being driven coherently for efficient excitation, are exemplified by a spherical swing with some phasemismatch between drive and response. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the response. Although a perioddoubling sequence, for damping increasing, leads to the attractor, this is actually born as a hard (as regards amplitude) bifurcation at a zero growthrate parametric line; as damping decreases, an unstable fixed point crosses an invariant plane to enter as saddlefocus a phasespace domain of physical solutions. A second hard bifurcation occurs at the zero mismatch line, the saddlefocus leaving that domain. Times on the attractor diverge when approaching either line, leading to exactly onedimensional and noninvertible limit maps, which are analytically determined.
 Publication:

Physica D Nonlinear Phenomena
 Pub Date:
 November 1993
 DOI:
 10.1016/01672789(93)901865
 Bibcode:
 1993PhyD...69..148S