This paper mainly studies the equivariant Hopf bifurcation of a delayed reaction–diffusion predator–prey model with stage structures on a two-dimensional circular domain. Firstly, we calculate the existence of steady-state solutions, and then analyze the existence of Hopf and equivariant Hopf bifurcation for the model according to bifurcation theory. Secondly, we calculate the normal form of the equivariant Hopf bifurcation. Finally, we conduct numerical simulations to verify the conclusion. And through simulation, we obtain a spatially homogeneous periodic solution, and spatially inhomogeneous periodic solution including rotating waves and standing waves on a two-dimensional circular domain, which shows rich dynamic properties on a two-dimensional space.
Gao et al. (Sat,) studied this question.