Global dynamics of the chemostat with different removal rates and variable yields
In this paper, we consider a competition model between $n$ species in a chemostat includingboth monotone and non-monotone growth functions, distinct removal rates and variable yields.We show that only the species with the lowest break-even concentration survives, provided that additional technicalco...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2011-05-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2011.8.827 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we consider a competition model between $n$ species in a chemostat includingboth monotone and non-monotone growth functions, distinct removal rates and variable yields.We show that only the species with the lowest break-even concentration survives, provided that additional technicalconditions on the growth functions and yields are satisfied.We construct a Lyapunov function which reduces to the Lyapunov function used byS. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760-763] in the Monod case when the growthfunctions are of Michaelis-Menten type and the yields are constant.Various applications are given including linear, quadratic and cubic yields. |
|---|---|
| ISSN: | 1551-0018 |