Stability and hopf bifurcation of a predator-prey model with discrete and distributed delays

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 the- ory and center manifold theorem, the explicit algorithm determining the stability, direction of the bifurcating periodic solutions are de- rived. Finally, we perform the numerical simulations for justifying the theoretical results. © 2017 Elsevier B.V., All rights reserved.