Stability and Hopf Bifurcation in a delayed ratio dependent Holling-Tanner type model

Abstract

In this study, a delayed ratio dependent Holling-Tanner type predator-prey model 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. © 2015 Elsevier B.V., All rights reserved.