  In this paper, the dynamics of a modified Leslie-Gower predator-prey system
with two delays and diffusion is considered. By calculating stability switching
curves, the stability of positive equilibrium and the existence of Hopf
bifurcation and double Hopf bifurcation are investigated on the parametric
plane of two delays. Taking two time delays as bifurcation parameters, the
normal form on the center manifold near the double Hopf bifurcation point is
derived, and the unfoldings near the critical points are given. Finally, we
obtain the complex dynamics near the double Hopf bifurcation point, including
the existence of quasi-periodic solutions on a 2-torus, quasi-periodic
solutions on a 3-torus, and strange attractors.
