GLOBAL STABILITY FOR A PHYTOPLANKTON-NUTRIENT SYSTEM
The model proposed by A. H. Taylor et al. [18] is discussed, with a view to determining the global asymptotic stability of the equilibria. The system consists of two autonomous differential equations, modeling the couple Phytoplankton-Nutrient with no delay on the recycling efficiency of nutrient by bacterial decomposition. Two distinct cases, persistence and extinction of phytoplankton are considered. In each case we will state the local and then the global stability of the equilibria by constructing an appropriate Lyapunov function and using the LaSalle's invariance principle. Also, in the case of extinction of phytoplankton we have introduced a supply of nutrient in the system and we have revealed the bloom of phytoplankton, which appears biologically in upwelling conditions.