Stability Results of a Flocculation Model Incorporating Size-Structured, Time Delay, and Control

This paper supplements the parts that were not detailed in the previous work. For the parts that have been proven in detail previously, only the conclusions are provided. In biological contexts, the significance of algal cell size and time delay in nutrient reproduction is crucial. Moreover, it is essential to exert control during algal flocculation harvesting and sewage treatment. Initially, we introduced a dimensionless flocculation model. Subsequently, we examined the presence of positive equilibrium states and investigated the equilibrium behavior of the model. Ultimately, numerical simulations demonstrated that the model exhibits backward bifurcation.