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Global dynamics of two phytoplankton-zooplankton models with toxic substances effect
Shanshan Chen,Hong Yang,Junjie Wei
Keywords:Phytoplankton-zooplankton, Global stability, Bistable phenomenon
Abstract:
      In this paper, we investigate phytoplankton-zooplankton models with toxic substances effect and two different kinds of predator functional responses. For Holling type II predator functional response, it is shown that the local stability of the positive equilibrium implies global stability if there exists a unique positive equilibrium. When there exist multiple positive equilibria, the local stability of the positive equilibrium with small phytoplankton population density implies that the model occurs bistable phenomenon. These results also hold for Holling type III predator functional response under certain conditions.