Asymptotic and Transient Mean-Square Properties of Stochastic Systems Arising in Ecology, Fluid Dynamics, and System Control

Abstract

We examine the role of persistent, state-dependent stochastic perturbations on the mean-square properties of nonnormal linear systems arising in three applications. In an example from population biology, we extend to the stochastic case measures of asymptotic and transient response of a predator-prey system to initial value perturbations and examine the relative effects on these measures of persistent stochastic perturbations of each species. In an example from fluid dynamics, we show how a linear stochastic mixing term may induce a transition-to-turbulence in certain low-dimensional models of plane Couette flow. Finally, we look at the role of drift-diffusion interaction effects in the noise-induced stabilization of a linear system with a single high-gain feedback control parameter.