A way to model stochastic perturbations in population dynamics models with bounded realizations

Abstract

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.

Corrigendum to the paper: A way to model stochastic perturbations in population dynamics models with bounded realizations. Commun Nonlinear Sci Numer Simulat, 77 (2019), 239–257

“…In our paper [3] we presented a new way to model real noisy perturbations by making use of the well-known Ornstein-Uhlenbeck (OU) process. In addition, we illustrated this idea with different examples coming from population dynamics and several numerical simulations.…”

“…Let us describe firstly the explanations given in Caraballo et al [3] in order to let the reader understand the error in Caraballo et al [3] and the changes needed to preserve the spirit and the goal of our original work.…”

“…Motivated by this fact, we presented in Caraballo et al [3] a way to model bounded real perturbations involving the OU process, which has proved to fit in a very loyal way the random disturbances observed in real life.…”

“…In order to deal with system (1) , we introduced in Caraballo et al [3] the OU process which is defined by the random variable…”

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