ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Switching Effect of Predation On Large Size Prey Species Exhibiting Group Defense


Q. J. A. Khan

Department of Mathematics & Statistics, College of Science,
Sultan Qaboos University, P. Box 36, PC - 123, Muscat,
Sultanate of Oman

B. S. Bhatt

Department Of Mathematics & Computer Science
The University Of The West Indies, St. Augustine,
Trindad & Tobago

R. P. Jaju

Department of Computer Science, Faculty of Science,
University Of Swaziland, P Bag 4, Kwaluseni,
Swaziland (Southern Africa)


A Mathematical model with one prey species living in two different habitats and a predator where a prey exhibits group defense is studied. The prey species is able to migrate between two different habitats due to change in seasonal conditions. The stability analysis is carried out for a critical point of the system where all species co-exist. Using rate of conversion of the prey to predator as bifurcation parameter, conditions for a Hopf bifurcation to occur are derived. It is shown numerically that predatory rate increases at low population density of prey species, has not always stabilizing effect for the prey-predator system.

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