Dynamics of a toxic producing phytoplankton–zooplankton model with three–dimensional patch

Abstract

In this paper, we perform a further dynamic analysis for a toxin–producing phytoplankton–zooplankton model proposed by Chattopadhyay et al. (2008), including the number of the positive equilibria, the stability of each equilibrium and possible bifurcations. Our findings indicate that the model can exhibit multiple bistability phenomena: between an interior equilibrium or an interior limit cycle and a boundary equilibrium, and undergo more complex bifurcations: Hopf, saddle–node and Bogdanov–Takens bifurcations.