Differential and Integral Equations

Competition for two essential resources with internal storage and periodic input

Sze-Bi Hsu, Feng-Bin Wang, and Xiao-Qiang Zhao

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Abstract

We study a mathematical model of two species competing in a chemostat for two internally stored essential nutrients, where the nutrients are added to the culture vessel by way of periodic forcing functions. Persistence of a single species happens if the nutrient supply is sufficient to allow it to acquire a threshold of average stored nutrient quota required for growth to balance dilution. More precisely, the population is washed out if a sub-threshold criterion holds, while there is a globally stable positive periodic solution, if a super-threshold criterion holds. When there is mutual invasibility of both semitrivial periodic solutions of the two-species model, both uniform persistence and the existence of periodic coexistence state are established.

Article information

Source
Differential Integral Equations Volume 29, Number 7/8 (2016), 601-630.

Dates
First available in Project Euclid: 3 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1462298678

Mathematical Reviews number (MathSciNet)
MR3498870

Zentralblatt MATH identifier
06604488

Subjects
Primary: 34C12: Monotone systems 34D20: Stability 34D23: Global stability

Citation

Hsu, Sze-Bi; Wang, Feng-Bin; Zhao, Xiao-Qiang. Competition for two essential resources with internal storage and periodic input. Differential Integral Equations 29 (2016), no. 7/8, 601--630. https://projecteuclid.org/euclid.die/1462298678.


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