An Multivariable Approach for the Chemostat Model

Sammanfattning: We use a multivariable approach to study the Chemostat model for a food chain. Using a Lyapunov function we reduce the system to a two-dimensional system.We then find isoclines and equilibrium points using a change of variables and the implicit function theorem.It turn out to be three equilibriums, namely the extinction equilibrium, caring capacity equilibrium and the implicit representation of an isocline where all solutions for the interior equilibrium is expressed.