Abstract. We show that two dynamical systems exhibiting very different deterministic behaviours possess very similar stationary distributions when stabilized by a multiplicative Gaussian white noise. We also discuss practical aspects of numerically simulating these systems. We show that there exists a noise level that is optimal in the sense that the interval during which discrete-time versions of the systems remain physical is maximized. Analytical results are illustrated by numerical examples.

Received 31 August 2004
Published 31 January 2005