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Discrete & Continuous Dynamical Systems - S
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A nutrient-prey-predator model: Stability and bifurcations

A nutrient-prey-predator model: stability and bifurcations
descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2020Embargo end date: 01 Jan 2018 English Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Discrete & Continuous Dynamical Systems - S, volume 13, pages 2,975-3,004 (issn: 1937-1179, Copyright policy )
Authors: Ballyk, Mary; Staffeldt, Ross; Jawarneh, Ibrahim;

doi: 10.3934/dcdss.2020192 , 10.48550/arxiv.1812.09964

arXiv: 1812.09964

A nutrient-prey-predator model: Stability and bifurcations

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.

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

Keywords

Bifurcations of singular points in dynamical systems, Bifurcation theory for ordinary differential equations, chemostat, Dynamical Systems (math.DS), Dynamical systems in biology, Primary 37G10, Secondary 34C23 92D25 34A34, Population dynamics (general), coexistence equilibrium, FOS: Mathematics, Hopf bifurcation, Mathematics - Dynamical Systems

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
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gold