Fluctuational phase-flip transitions in parametrically driven oscillators

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Abstract
We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of the transitions is analyzed as a function of frequency detuning and field amplitude scaled by the damping and nonlinearity parameters of the oscillator. Both fourth- and sixth-order nonlinearities are taken into account. The parameter ranges where the system is bistable and tristable are investigated. Explicit results are obtained in the limit of small damping, or equivalently, strong driving, including scaling near bifurcation points.

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