Abstract
This paper concerns a discrete-time phytoplankton–zooplankton model in which the effects of toxin produced by phytoplankton and refuges provided for phytoplankton on the interactions between phytoplankton and zooplankton are considered. We first discuss the existence and stability of fixed points. When two parameters change, it is shown that there exist some codimension-two bifurcations, including fold-flip bifurcation and strong resonance bifurcations. Moreover, we give the corresponding bifurcation diagrams, phase diagrams and maximum Lyapunov exponent diagrams. The results show that phytoplankton toxin and refuges play important roles in the occurrence and termination of algal blooms in freshwater lakes.
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