Abstract
In this paper, we study a predatorprey model which has one prey and two predators with BeddingtonDeAngelis functional responses. Firstly, we establish a set of sufficient conditions for the permanence and extinction of species. Secondly, the periodicity of positive solutions is studied. Thirdly, by using Liapunov functions and the continuation theorem in coincidence degree theory, we show the global asymptotic stability of such solutions. Finally, we give some numerical examples to illustrate the behavior of the model.
| Original language | English |
|---|---|
| Pages (from-to) | 4868-4881 |
| Number of pages | 14 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 74 |
| Issue number | 14 |
| DOIs | |
| Publication status | Published - Oct 1 2011 |
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All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Cite this
Dynamics of species in a model with two predators and one prey. / Ton, Ta Viet; Hieu, Nguyen Trong.
In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 74, No. 14, 01.10.2011, p. 4868-4881.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Dynamics of species in a model with two predators and one prey
AU - Ton, Ta Viet
AU - Hieu, Nguyen Trong
PY - 2011/10/1
Y1 - 2011/10/1
N2 - In this paper, we study a predatorprey model which has one prey and two predators with BeddingtonDeAngelis functional responses. Firstly, we establish a set of sufficient conditions for the permanence and extinction of species. Secondly, the periodicity of positive solutions is studied. Thirdly, by using Liapunov functions and the continuation theorem in coincidence degree theory, we show the global asymptotic stability of such solutions. Finally, we give some numerical examples to illustrate the behavior of the model.
AB - In this paper, we study a predatorprey model which has one prey and two predators with BeddingtonDeAngelis functional responses. Firstly, we establish a set of sufficient conditions for the permanence and extinction of species. Secondly, the periodicity of positive solutions is studied. Thirdly, by using Liapunov functions and the continuation theorem in coincidence degree theory, we show the global asymptotic stability of such solutions. Finally, we give some numerical examples to illustrate the behavior of the model.
UR - http://www.scopus.com/inward/record.url?scp=79957889029&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79957889029&partnerID=8YFLogxK
U2 - 10.1016/j.na.2011.04.061
DO - 10.1016/j.na.2011.04.061
M3 - Article
AN - SCOPUS:79957889029
VL - 74
SP - 4868
EP - 4881
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 14
ER -