COHERENT STRUCTURES IN A POPULATION MODEL FOR MUSSEL-ALGAE INTERACTION. ANNA GHAZARYAN AND VAHAGN MANUKIAN Abstract. We consider a known model that describes formation of mussel beds on soft sediments. The model consists of nonlinearly coupled pdes 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. 1. Introduction The ability of mussels to self-organize has been known to the ecologists (see [14] and references within). In recent years, a significant interest towards using mathematics to understand the mechanisms of the phenomenon of aggregation and pattern formation in mussel beds has been noticeable. Predator-prey models have been suggested to explain pattern formation in mussel beds. Some of them are restricted to mussel and algae interactions [14, 15], some, in addition, include a description of sediment accumulation [11]. In an important work [10] the role of the phase separation in pattern formation on mussel beds was pointed out. Cahn-Hilliard equation was demonstrated to successfully describe patterns observable in field experiments. In [10] density-dependent movement as opposed to scale- dependent activator-inhibitor feedback is recognized the first time as a general mechanism of pattern formation in ecology. The dynamics illustrated by Cahn-Hilliard equation captures interpolation between two stable phases that happens on short-time scales rather than the intermediate or long-range dynamics induced by an instability of a phase. Current work is concentrated on the two-component partly parabolic system of partial dif- ferential equations related to the system introduced in [14] which we describe below. The scaling that we use in this system is effective for longer time scales compared to the ones studied in [10]. On such time scales as it is mentioned in [10] the mortality and individual growth of mussels dominate the shape of the mussel bed. Date : August 21, 2014. 1