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In this paper, the dynamics of a modified Leslie-Gower predator-prey systemwith two delays and diffusion is considered. By calculating stability switchingcurves, the stability of positive equilibrium and the existence of Hopfbifurcation and double Hopf bifurcation are investigated on the parametricplane of two delays. Taking two time delays as bifurcation parameters, thenormal form on the center manifold near the double Hopf bifurcation point isderived, and the unfoldings near the critical points are given. Finally, weobtain the complex dynamics near the double Hopf bifurcation point, includingthe existence of quasi-periodic solutions on a 2-torus, quasi-periodicsolutions on a 3-torus, and strange attractors.

Two delays induce Hopf bifurcation and double Hopf bifurcation in a diffusive Leslie-Gower predator-prey system