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^*

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

36 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

ASJC Scopus subject areas

Neuroscience(all)
Immunology
Mathematics(all)
Biochemistry, Genetics and Molecular Biology(all)
Environmental Science(all)
Pharmacology
Agricultural and Biological Sciences(all)
Computational Theory and Mathematics

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10.1016/j.bulm.2003.08.005

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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'.",

author = "Khan, {Q. J.A.} and E. Balakrishnan and Wake, {G. C.}",

note = "Funding Information: Q J A Khan is grateful to the Sultan Qaboos University for financially supporting the research IG/SCI/DOMAS/01/03.",

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AU - Wake, G. C.

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Analysis of a predator-prey system with predator switching

Abstract

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