Bifurcation analysis of an algal blooms dynamical model in trophic interaction

In this paper, we revisit the algal blooms model of plankton interactions initially proposed by Das and Sarkar (DCDIS-A, 14(3):401–414, 2007), where the oscillatory mode in the interaction between phytoplankton and zooplankton is observed. We provide a detailed analysis of the dependence of the equilibria and their stability on various parameters in the model. The bifurcation behaviors around equilibrium (e.g., Hopf bifurcation, Bogdanov–Takens bifurcation) are further found. Meanwhile, numerical simulations verify and illustrate the effectiveness of our theoretical results.