Dynamical Analysis in a Delayed Predator-Prey Model with Two Delays

Abstract EN

A class of Beddington-DeAngelis functional response predator-prey model is considered.

The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived.

Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory.

Some numerical simulations for justifying the theoretical analysis are also provided.

Finally, main conclusions are given.