2025/01/14 by Alvarez-Latuz, Claudia, Bayen, Terence, Coville, Jerome
#34A34 #34D23 #37C75 #93D99 #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2501.08011
This paper is devoted to the analysis of global stability of the chemostat system with a perturbation term representing any type of exchange between species. This conversion term depends on species and substrate concentrations but also on a positive perturbation parameter. After having written the invariant manifold as a union of a family of compact subsets, our main result states that for each subset in this family, there is a positive threshold for the perturbation parameter below which, the system is globally asymptotically stable in the corresponding subset. Our approach relies on the Malkin-Gorshin Theorem and on a Theorem by Smith and Waltman about perturbations of a globally stable steady state. Properties of steady-states and numerical simulations of the system's asymptotic behavior complete this study for two types of perturbation term between species.