Fluctuational transitions between stable states of a nonlinear oscillator driven by random resonant force

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Abstract
Fluctuations of a nonlinear oscillator driven by an intense resonant field with fluctuating phase are considered in the region of bistability. The general expression for the probability of a fluctuational transition between stable states is found to logarithmic accuracy. In the weak-damping limit the probabilities are obtained in the explicit form including both the argument of the exponential and the preexponential factor. A simple general method of determining the latter for underdamped systems is suggested. The probability of an escape from a metastable state near the bifurcation point where this state disappears is analyzed. The low-frequency susceptibility of the oscillator is shown to have a peculiar structure in the region of parameters where the stationary populations of the stable states are of the same order of magnitude. The stochastic modulation of the phase of an oscillator due to coupling to a bath is considered and its consequences are compared to those of randomness of the phase of a driving field.