Dynamical analysis of a toxin-producing phytoplankton-zooplankton model with refuge
Juan Li Yongzhong Song Hui Wan Huaiping Zhu
Mathematical Biosciences & Engineering 2017, 14(2): 529-557 doi: 10.3934/mbe.2017032

To study the impacts of toxin produced by phytoplankton and refuges provided for phytoplankton on phytoplankton-zooplankton interactions in lakes, we establish a simple phytoplankton-zooplankton system with Holling type Ⅱ response function. The existence and stability of positive equilibria are discussed. Bifurcation analyses are given by using normal form theory which reveals reasonably the mechanisms and nonlinear dynamics of the effects of toxin and refuges, including Hopf bifurcation, Bogdanov-Takens bifurcation of co-dimension 2 and 3. Numerical simulations are carried out to intuitively support our analytical results and help to explain the observed biological behaviors. Our findings finally show that both phytoplankton refuge and toxin have a significant impact on the occurring and terminating of algal blooms in freshwater lakes.

keywords: Phytoplankton zooplankton refuge toxin algal blooms multiple equilibria stability Hopf bifurcation Bogdanov-Takens bifurcation

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