Spatiotemporal Patterns in a Delayed Reaction–Diffusion Mussel–Algae Model

Abstract

We study the spatiotemporal patterns of a delayed reaction–diffusion mussel–algae system subject to Neumann boundary conditions. This paper is a continuation of our previous studies on the mussel–algae model. We prove the global existence and positivity of solutions. By analyzing the distribution of eigenvalues, we obtain the stability conditions for the positive constant steady state, the existence of Hopf bifurcation and the Turing instability. We show the dynamic classification near the Turing–Hopf singularity in the dimensionless parameter space and observe a transiently spatially nonhomogeneous periodic solution in simulations. Both theoretical and numerical results reveal that the Turing–Hopf bifurcation can enrich the diversity of the spatial distribution of populations.