English

A Nutrient-Prey-Predator Model: Stability and Bifurcations

Dynamical Systems 2019-11-20 v2

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.

Keywords

Cite

@article{arxiv.1812.09964,
  title  = {A Nutrient-Prey-Predator Model: Stability and Bifurcations},
  author = {Mary Ballyk and Ibrahim Jawarneh and Ross Staffeldt},
  journal= {arXiv preprint arXiv:1812.09964},
  year   = {2019}
}

Comments

Version 2 corrects inequalities on page 7 that were backwards in Version 1

R2 v1 2026-06-23T06:55:28.614Z