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Title: Bifurcation and Stability in a Delayed Predator-Prey Model with Mixed Functional Responses
Authors: Yafia, R.
Aziz-Alaoui, M. A.
Merdan, Hüseyin
Tewa, J. J.
Keywords: Predator prey model
mixed functional responses
delay differential equations
local and global stability
Hopf bifurcation
Issue Date: Jun-2015
Publisher: World Scientific Publishing Co. Pte Ltd
Source: Yafia, R., Aziz-Alaoui, M. A., Merdan, H., & Tewa, J. J. (2015). Bifurcation and Stability in a Delayed Predator–Prey Model with Mixed Functional Responses. International Journal of Bifurcation and Chaos, 25(07), 1540014.
Abstract: The model analyzed in this paper is based on the model set forth by Aziz Alaoui et al. [Aziz Alaoui & Daher Okiye, 2003; Nindjin et al., 2006] with time delay, which describes the competition between the predator and prey. This model incorporates a modified version of the Leslie-Gower functional response as well as that of Beddington-DeAngelis. In this paper, we consider the model with one delay consisting of a unique nontrivial equilibrium E* and three others which are trivial. Their dynamics are studied in terms of local and global stabilities and of the description of Hopf bifurcation at E*. At the third trivial equilibrium, the existence of the Hopf bifurcation is proven as the delay (taken as a parameter of bifurcation) that crosses some critical values.
ISSN: 0218-1274
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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