Resonant dynamics of nonlinear stochastic systems

The impact of random perturbations on resonant motions in nonlinear oscillatory systems is studied. It is shown that the reliability of resonant systems can be associated with stable motions within a small near resonant domain (effect of "capture in resonance"). The model of near resonant motions in stochastic systems is given, and asymptotic analysis of this model is developed. It is demonstrated that the capture phenomenon is closely tied with the dissipation of the mean energy in the near resonant domain. The necessary conditions for capture in resonance in presence of random perturbations are constructed.