AUTHOR: Roy-R-V. Nauman-E.
INSTITUTION: Univ of Delaware, Newark, DE, USA.
SOURCE: Journal of Sound and Vibration v 183 n 2 Jun 1 1995. p
PUBLICATION: JA (Journal Article).
We examine various
phenomena induced by white Gaussian random perturbations
in the response of nonlinear dynamical systems. In the first part of this
work, digital and analog experiments are conducted on a simple
single-degree-of-freedom oscillator with piecewise linear restoring force
and harmonic forcing. They reveal that small noise perturbations can give
rise to large deviations of the response which ultimately lead to
transitions between the coexisting attractors of the unperturbed system.
These transitions are analyzed probabilistically by determining the mean
time spent by the trajectories to exit from the basin of a given
attractor. By determining the relationship between mean
first-exit time and noise intensity, it is found that each
attractor can be characterized by an activation energy which
yields a measure of its relative stability. We also find that, even in the
case of a single attractor, weak noise can induce large excursions to sets
of the state space (chaotic semi-attractor) which are otherwise globally
repelling in the absence of noise. In the second part of this work, some
results obtained numerically are shown to be predicted theoretically by
the use of asymptotic analyses of the randomly perturbed response of
dynamical systems in the limit of weak noise. These techniques provide a
generalization of the notion of potential to non-potential, non-equlibrium
systems. In particular, the notion of activation energy is verified
theoretically, and its determination may be possible without massive