  In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model
dynamical systems subjected to bounded noisy perturbations. In order to discuss
the main characteristics of this new approach we consider some basic models in
population dynamics such as the logistic equations and competitive
Lotka-Volterra systems. The key is the fact that these perturbations can be
ensured to keep inside some interval that can be previously fixed, for
instance, by practitioners, even though the resulting model does not generate a
random dynamical system. However, one can still analyze the forwards asymptotic
behavior of these random differential systems. Moreover, to illustrate the
advantages of this type of modeling, we exhibit an example testing the
theoretical results with real data, and consequently one can see this method as
a realistic one, which can be very useful and helpful for scientists.
