Abstract
We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 481-515 |
| Number of pages | 35 |
| Journal | Journal of Mathematical Biology |
| Volume | 55 |
| Issue number | 4 |
| DOIs | |
| State | Published - Oct 2007 |
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Keywords
- Bi-stability
- Chemostat
- Coexistence
- Competition
- Competitive exclusion
- Essential resources
- Resource storage
ASJC Scopus subject areas
- Agricultural and Biological Sciences (miscellaneous)
- Mathematics (miscellaneous)
Cite this
Global dynamics of microbial competition for two resources with internal storage. / Li, Bingtuan; Smith, Hal.
In: Journal of Mathematical Biology, Vol. 55, No. 4, 10.2007, p. 481-515.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Global dynamics of microbial competition for two resources with internal storage
AU - Li, Bingtuan
AU - Smith, Hal
PY - 2007/10
Y1 - 2007/10
N2 - We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model.
AB - We study a chemostat model that describes competition between two species for two essential resources based on storage. The model incorporates internal resource storage variables that serve the direct connection between species growth and external resource availability. Mathematical analysis for the global dynamics of the model is carried out by using the monotone dynamical system theory. It is shown that the limiting system of the model basically exhibits the familiar Lotka-Volterra alternatives: competitive exclusion, coexistence, and bi-stability, and most of these results can be carried over to the original model.
KW - Bi-stability
KW - Chemostat
KW - Coexistence
KW - Competition
KW - Competitive exclusion
KW - Essential resources
KW - Resource storage
UR - http://www.scopus.com/inward/record.url?scp=34548588283&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=34548588283&partnerID=8YFLogxK
U2 - 10.1007/s00285-007-0092-8
DO - 10.1007/s00285-007-0092-8
M3 - Article
C2 - 17505828
AN - SCOPUS:34548588283
VL - 55
SP - 481
EP - 515
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
SN - 0303-6812
IS - 4
ER -