Corrigendum to the chapter "Some aspects concerning the dynamics of stochastic chemostats"

TL;DR

This paper corrects a previous stochastic chemostat model by fixing an error, then reanalyzes the system using random attractors and numerical simulations to provide accurate insights into its dynamics.

Contribution

It revises an earlier stochastic chemostat model with corrected equations and offers a comprehensive analysis using random attractors and numerical methods.

Findings

Corrected the stochastic chemostat model equations.

Established existence of unique solutions for the corrected system.

Demonstrated the presence of random attractors through analysis and simulations.

Abstract

In this paper we correct an error made in a previous work, where a misleading stochastic system was obtained due to a lapse concerning a sign in one of the equations at the beginning of the work such that the results obtained are quite different to the ones developed throughout this paper since the required conditions, and also the results, substantially change. Then, in this work we repair the analysis carried out there, where we studied a simple chemostat model influenced by white noise by making use of the theory of random attractors. Even though the changes are minor, we have chosen to provide a new version of the entire paper instead of a list of changes, for sake of readability. We first perform a change of variable using the Ornstein-Uhlenbeck process, transforming our stochastic model into a system of differential equations with random coefficients. After proving that this random system possesses a unique solution for any initial value, we analyze the existence of random attractors. Finally we illustrate our results with some numerical simulations.