Global Dynamics of Modeling Flocculation of Microorganism

From a biological perspective, a dynamic model describing the cultivation and flocculation of a microorganism that uses two different kinds of nutrients (carbon source and nitrogen source) is proposed. For the proposed model, there always exists a boundary equilibrium, i.e., Rhodopseudomonas palustris -free equilibrium. Furthermore, under additional conditions, the model also has five positive equilibria at most, i.e., the equilibria for which carbon source, nitrogen source, Rhodopseudomonas palustris and flocculants are coexistent. The phenomena of backward and forward bifurcations are extensively discussed by using center manifold theory. The global stability of the boundary equilibrium of the proposed model is deeply investigated. Moreover, the local stability of the positive equilibrium and the uniform persistence of the proposed model are discussed. Under additional conditions, the global stability of the positive equilibrium is studied. Some control strategies are given by the theoretical analysis. Finally, some numerical simulations are performed to confirm the correctness of the theoretical results.