  In this paper, we consider the dynamics of a delayed reaction-diffusion
mussel-algae system subject to Neumann boundary conditions. When the delay is
zero, we show the existence of positive solutions and the global stability of
the boundary equilibrium. When the delay is not zero, we obtain the stability
of the positive constant steady state and the existence of Hopf bifurcation by
analyzing the distribution of characteristic values. By using the theory of
normal form and center manifold reduction for partial functional differential
equations, we derive an algorithm that determines the direction of Hopf
bifurcation and the stability of bifurcating periodic solutions. Finally, some
numerical simulations are carried out to support our theoretical results.
