Analysis of a predator-prey system with predator switching

Q. J A Khan; E. Balakrishnan; G. C. Wake

doi:10.1016/j.bulm.2003.08.005

Analysis of a predator-prey system with predator switching

Q. J A Khan, E. Balakrishnan, G. C. Wake

Mathematics & Statistics

Research output: Contribution to journal › Article

25 Citations (Scopus)

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	https://doi.org/10.1016/j.bulm.2003.08.005
Publication status	Published - Jan 2004

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ASJC Scopus subject areas

Agricultural and Biological Sciences(all)

Cite this

Khan, Q. J. A., Balakrishnan, E., & Wake, G. C. (2004). Analysis of a predator-prey system with predator switching. Bulletin of Mathematical Biology, 66(1), 109-123. https://doi.org/10.1016/j.bulm.2003.08.005

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10.1016/j.bulm.2003.08.005