Bifurcation Analysis in a Class of Delayed Predator-Prey Models

A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, the existence of Hopf bifurcation are obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.