Modeling and stability analysis of a microalgal pond with nitrification

Microalgae culture fed with ammonium may face the presence of nitrifying bacteria. The aim of this paper is to propose and analyze a nonlinear system which represents the dynamics of these two species (microalgae and nitrifying bacteria) in competition for nitrogen (present as ammonium and nitrate produced by nitrification) in a continuous process. The existence and local stability of system equilibria is studied. Reduction by conservation principle, perturbed systems and Lyapunov methods are used to provide sufficient conditions for the global asymptotic stability of the system equilibria. Finally, we illustrate our analysis with a case study, showing which operating conditions (dilution rate and pond depth) can promote the presence of nitrifiers with microalgae.