Mathematical analysis of a modified Volterra-Leslie chemostat Model

Abstract

In this paper, we investigate the asymptotic behavior of a modified chemostat model. We first demonstrate the existence of equilibria. Then, we present a mathematical analysis for the model, the invariance, the positivity, the persistence of the solutions, and the asymptotic global stability of the interior equilibrium. Some numerical simulations are carried out to illustrate the main results.

Keywords: Asymptotic stability; Chemostat; Dissipativity; Persistence, permanence; Volterra-Leslie model.