In this paper, a flocculation model is considered in a chemostat with a single resource and one species in two forms: planktonic and aggregated bacteria. The removal rates are distinct and include the specific death rates. Considering distinct yield coefficients with a large class of growth rates, we present a mathematical analysis of the model by establishing the necessary and sufficient conditions of the existence and local asymptotic stability of all steady states. From these conditions, we first determine theoretically the operating diagram describing the asymptotic behavior of the system according to the two operating parameters. The bifurcations analysis shows a rich behavior: transcritical, saddle-node, Hopf, and homoclinic bifurcations. Using the numerical method with MATCONT software, we detect other types of two-parameter bifurcations such as Bogdanov-Takens and Cusp bifurcations. Our analysis shows that the flocculation process promotes the coexistence of isolated and attached bacteria around a stable limit cycle or a positive steady state. These theoretical messages explain and reinforce the experimental observations about the positive effect of flocculation on the maintenance of species coexistence and the protection of the most relevant species among microbial ecosystems.