Abstract
In this paper, we consider an interaction of prey and predator species where prey species have the ability of group defence. Thresholds, equilibria and stabilities are determined for the system of ordinary differential equations. Taking carrying capacity as a bifurcation parameter, it is shown that a Hopf bifurcation can occur implying that if the carrying capacity is made sufficiently large by enrichment of the environment, the model predicts the eventual extinction of the predator providing strong support for the so-called 'paradox of enrichment'.
| Original language | English |
|---|---|
| Pages (from-to) | 109-123 |
| Number of pages | 15 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 66 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2004 |
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ASJC Scopus subject areas
- Agricultural and Biological Sciences(all)
Cite this
Analysis of a predator-prey system with predator switching. / Khan, Q. J A; Balakrishnan, E.; Wake, G. C.
In: Bulletin of Mathematical Biology, Vol. 66, No. 1, 01.2004, p. 109-123.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Analysis of a predator-prey system with predator switching
AU - Khan, Q. J A
AU - Balakrishnan, E.
AU - Wake, G. C.
PY - 2004/1
Y1 - 2004/1
N2 - In this paper, we consider an interaction of prey and predator species where prey species have the ability of group defence. Thresholds, equilibria and stabilities are determined for the system of ordinary differential equations. Taking carrying capacity as a bifurcation parameter, it is shown that a Hopf bifurcation can occur implying that if the carrying capacity is made sufficiently large by enrichment of the environment, the model predicts the eventual extinction of the predator providing strong support for the so-called 'paradox of enrichment'.
AB - In this paper, we consider an interaction of prey and predator species where prey species have the ability of group defence. Thresholds, equilibria and stabilities are determined for the system of ordinary differential equations. Taking carrying capacity as a bifurcation parameter, it is shown that a Hopf bifurcation can occur implying that if the carrying capacity is made sufficiently large by enrichment of the environment, the model predicts the eventual extinction of the predator providing strong support for the so-called 'paradox of enrichment'.
UR - http://www.scopus.com/inward/record.url?scp=0842349505&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0842349505&partnerID=8YFLogxK
U2 - 10.1016/j.bulm.2003.08.005
DO - 10.1016/j.bulm.2003.08.005
M3 - Article
VL - 66
SP - 109
EP - 123
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
IS - 1
ER -