Abstract
We consider plankton-nutrient interaction models consisting of phytoplankton, herbivorous zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non-negative equilibria, as well as persistence are given. We also consider the zooplankton-phytoplankton-nutrient interaction models with a fluctuating nutrient input and with a periodic washout rate, respectively. It is shown that coexistence of the zooplankton and phytoplankton may arise due to positive bifurcating periodic solutions.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 633-654 |
| Number of pages | 22 |
| Journal | Journal of Mathematical Biology |
| Volume | 31 |
| Issue number | 6 |
| DOIs | |
| State | Published - 1993 |
| Externally published | Yes |
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Keywords
- Bifurcation
- Coexistence
- Fluctuating nutrient input
- Nutrient recycling
- Persistence
ASJC Scopus subject areas
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics
- Modeling and Simulation
Cite this
Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling. / Ruan, Shigui.
In: Journal of Mathematical Biology, Vol. 31, No. 6, 1993, p. 633-654.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling
AU - Ruan, Shigui
PY - 1993
Y1 - 1993
N2 - We consider plankton-nutrient interaction models consisting of phytoplankton, herbivorous zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non-negative equilibria, as well as persistence are given. We also consider the zooplankton-phytoplankton-nutrient interaction models with a fluctuating nutrient input and with a periodic washout rate, respectively. It is shown that coexistence of the zooplankton and phytoplankton may arise due to positive bifurcating periodic solutions.
AB - We consider plankton-nutrient interaction models consisting of phytoplankton, herbivorous zooplankton and dissolved limiting nutrient with general nutrient uptake functions and instantaneous nutrient recycling. For the model with constant nutrient input and different constant washout rates, conditions for boundedness of the solutions, existence and stability of non-negative equilibria, as well as persistence are given. We also consider the zooplankton-phytoplankton-nutrient interaction models with a fluctuating nutrient input and with a periodic washout rate, respectively. It is shown that coexistence of the zooplankton and phytoplankton may arise due to positive bifurcating periodic solutions.
KW - Bifurcation
KW - Coexistence
KW - Fluctuating nutrient input
KW - Nutrient recycling
KW - Persistence
UR - http://www.scopus.com/inward/record.url?scp=0002427184&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0002427184&partnerID=8YFLogxK
U2 - 10.1007/BF00161202
DO - 10.1007/BF00161202
M3 - Article
AN - SCOPUS:0002427184
VL - 31
SP - 633
EP - 654
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
SN - 0303-6812
IS - 6
ER -