Coherent Structures in a Population Model for Mussel-Algae Interaction

We consider a known model that describes formation of mussel beds on soft sediments. The model consists of nonlinearly coupled partial differential equations that capture evolution of mussel biomass on the sediment and algae in the water layer overlying the mussel bed. The system accounts for the diffusive spread of mussels, while the diffusion of algae is neglected and at the same time the tidal flow of the water is considered to be the main source of transport for algae but does not affect mussels. Therefore, both the diffusion and the advection matrices in the system are singular. A numerical investigation of this system in some parameter regimes is known. We present a systematic analytic treatment of this model. Among other techniques, we use geometric singular perturbation theory to analyze the nonlinear mechanisms of pattern and wave formation in this system.