2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25512We 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.New Journal of Physics, submittedStatistical Mechanicstext