Persistence criteria for a chemostat with variable nutrient input and variable washout with delayed response in growth

TL;DR

This paper analyzes a delayed chemostat model with variable nutrient input and washout, establishing persistence conditions that extend previous results and include periodic cases without delay restrictions.

Contribution

It provides necessary and sufficient persistence criteria for a chemostat with delay and variable inputs, generalizing prior work and including periodic scenarios.

Findings

Persistence criteria are derived for chemostats with delay and variable inputs.

In periodic cases, persistence depends on average input and washout rates.

No restrictions on delay size are needed for the criteria to hold.

Abstract

We study a general chemostat model with a discrete-time delay between consumption and growth. The goal of this article is to provide sufficient and necessary conditions for persistence. This extends previous works in the matter. Furthermore, in the particular case of periodic nutrient input and the same periodic washout with delayed response in growth, the persistence criteria are average criteria. We remark in no case we need to impose any restrictions on the size of the delay.