Bifurcation analysis in a modified Lesile–Gower model with Holling type II functional response and delay

In this paper, a modified Lesile–Gower predator–prey system with delay is considered. The existence of Hopf bifurcations at the positive equilibrium is established by analyzing the distribution of the characteristic values. Furthermore, different to previous papers, a multiple time scale technique is employed to calculate the normal form on the center manifold of delay differential equations, which is much easier to implement in practice than the conventional method, center manifold reduction. Finally, to verify our theoretical predictions, some numerical simulations are also included.