Journal of Applied Nonlinear Dynamics
Stability and Hopf Bifurcation of a PredatorPrey Model with Discrete and Distributed Delays
Journal of Applied Nonlinear Dynamics 5(1) (2016) 7391  DOI:10.5890/JAND.2016.03.006
Canan Çelik$^{1}$; Emine Degirmenci$^{2}$
Department of Mathematical Engineering, Bahçeşehir University, Istanbul, Turkey
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Abstract
In this study, a delayed ratio dependent predatorprey model with both discrete and distributed delays is investigated. First, the local stability of a positive equilibrium is studied and then the existence of Hopf bifurcations is established. By using the normal form theory and center manifold theorem, the explicit algorithm determining the stability, direction of the bifurcating periodic solutions are derived. Finally, we perform the numerical simulations for justifying the theoretical results.
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