Patterns Observed on Mussel Bed Formation

Student: Chloe Mattila

Major: Mathematics

Mentors: Dr. Stéphane Lafortune

Department: Mathematics

Patterns Observed on Mussel Bed Formation

The general goal of the project is to study a model which describes the formation of mussel beds on soft sediments. The model, which we will call the Mussel Model, captures the evolution of mussel biomass on the sediment and algae concentration in the water layer overlying the mussel bed. The model is used to give an explanation to interesting patterns observed in mussel beds on soft sediments in the Wadden Sea. The Mussel Model consists of two differential equations, that is they are equations involving derivatives. The {\bf{solutions}} to those equations represent possible behaviors for the mussel biomass as it interacts with the surrounding algae. The goal is to study the stability properties of the solutions. Stability is a fundamental concept, which can be illustrated by trying to make a pencil stand on its lead. Because it is such an unstable state, it is possible in theory only and cannot be observed in reality. The concept of stability carries over to differential equations and its study often involves sophisticated mathematical tools. The study of stability is important because it can distinguish the solutions that be observed in nature from the ones that cannot. In the research described in this proposal, we will tackle the problem of studying the stability of the solutions of the Mussel Model.