TITLE: Noise-Induced Transitions in Weakly Nonlinear Oscillators Near Resonance


SOURCE: Journal of Applied Mechanics, Transactions ASME v 62 n 2 Jun 1995. p 496-504.

YEAR: 1995.

PUBLICATION: JA (Journal Article).


The noise-induced transitions between the oscillatory steady states of a class of weakly nonlinear oscillators excited by resonant harmonic forcing is investigated. A set of averaged equations is derived governing slow variables of the system when the latter is perturbed by both additive white Gaussian noise and by random phase fluctuations of the resonant excitation. The behaviour of the reduced system in the case of cubic stiffness and viscous damping forces is investigated including the case of weak damping, the case of near bifurcation and the more general case when neither of the first two situations apply. In each case, the quasi-stationary probability density of the response and the mean time taken by the trajectories to pass from one basin of attraction to the other is predicted based on averaging of a near-Hamiltonian system in the weak damping limit, on center-manifold theory in the near-bifurcation case, or on Wentzell-Kramers-Brillouin (WKB) singular perturbation expansions in the more general case. These predictions are compared with digital simulations which show excellent agreement. 19 Refs.