Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems.

摘要: We consider the effect on a generic period-doubling bifurcation of periodic perturbation, whose frequency ${\ensuremath{\omega}}_{1}$ is near period-doubled ${\ensuremath{\omega}}_{0}$/2. The perturbation shown to always suppress bifurcation, shifting point and stabilizing behavior at original point. derive an equation characterizing response system analysis which reveals many interesting features perturbed including (1) scaling law relating shift amplitude (2) characteristics system's as function parameter, (3) parametric amplification signal nonlinear effects such gain saturation discontinuity in critical amplitude, (4) detuning (${\ensuremath{\omega}}_{1}$-${\ensuremath{\omega}}_{0}$/2) (5) emergence closely spaced set peaks spectrum. An important application use systems small-signal amplifiers, e.g., superconducting Josephson amplifier.