ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Stability and Hopf Bifurcation of a Predator-Prey Model with Discrete and Distributed Delays

Journal of Applied Nonlinear Dynamics 5(1) (2016) 73--91 | DOI:10.5890/JAND.2016.03.006

Canan Çelik$^{1}$; Emine Degirmenci$^{2}$

Department of Mathematical Engineering, Bahçeşehir University, Istanbul, Turkey

Abstract

In this study, a delayed ratio dependent predator-prey 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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