Global dynamics of a time-delayed microorganism flocculation model with saturated functional responses (Q1994011)

A time-delayed micro-organism flocculation model with saturated functional responses is considered. First, the local asymptotic stability of all equilibria for the model under consideration is proced and a threshold parameter, which governs the unsustainability and sustainability for the collection of micro-organisms, is studied. Then the authors study the global stability of this model by means of Lyapunov-LaSalle theorem. Moreover, the forward and backward bifurcations of the model are investigated. An explicit estimation of the lower bound for the micro-organism concentration is obtained as well.