Stability and Hopf Bifurcation in Predator-Prey Model with Modified Leslie-Gower and Beddington-DeAngelis Functional Response
AbstractThe model analyzed in this paper is based on the model set forthby M. A. Aziz Alaoui et al.В with time delay,which describes the competition between the predator and prey.This model incorporates a modified version of Leslie-Gowerfunctional response as well as that of the Beddington-DeAngelis.In this paper we consider the model with one delay and a uniquenon trivial equilibrium E* and the three others are trivial.Their dynamics are studied in terms of the local and globalstability and of the description of the Hopf bifurcation at E* and at the third trivial equilibrium, that is proven toexists as the delay (taken as a parameter of bifurcation) crossessome critical values.
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