NONPERIODIC DRIVING OF COUPLED OSCILLATORS - A SPHERICAL SWING

Nonlinearly coupled, damped oscillators at 1:1 frequency ratio, one os cillator being driven coherently for efficient excitation, are exempli fied by a spherical swing with some phase-mismatch between drive and r esponse. For certain damping range, excitation is found to succeed if it lags behind, but to produce a chaotic attractor if it leads the res ponse. Although a period-doubling sequence, for damping increasing, le ads to the attractor, this is actually born as a hard (as regards ampl itude) bifurcation at a zero growth-rate parametric line; as damping d ecreases, an unstable fixed point crosses an invariant plane to enter as saddle-focus a phase-space domain of physical solutions. A second h ard bifurcation occurs at the zero mismatch line, the saddle-focus lea ving that domain. Times on the attractor diverge when approaching eith er line, leading to exactly one-dimensional and noninvertible limit ma ps, which are analytically determined.