# A Nutrient-Prey-Predator Model: Stability and Bifurcations

## TL;DR

This paper analyzes a nutrient-prey-predator model in a chemostat, examining how nutrient levels influence system stability and bifurcations, including Hopf bifurcations and limit cycles, with analytical and numerical methods.

## Contribution

It provides a comprehensive analysis of stability and bifurcations in a nutrient-prey-predator system with general functional responses, including analytical verification and numerical illustrations.

## Key findings

- Identification of conditions for Hopf bifurcation
- Existence of limit cycles under certain nutrient levels
- Analytical and numerical validation of bifurcation scenarios

## Abstract

In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated equilibria and in their stability, as well as the global dynamics, as the nutrient concentration varies. The bifurcations of the system are analytically verified and we identify conditions under which an equilibrium undergoes a Hopf bifurcation and a limit cycle appears. Numerical simulations for specific functional responses illustrate the general results.