Simple-zero singularity in toxic phytoplankton-zooplankton model

Abstract

In this paper, we have considered a phytoplankton-zooplankton system with toxic liberation delay. Firstly, we give the critical values of transcritical bifurcation. Then, we derive the normal forms and their unfolding with original parameters in the system near the bifurcation point by the normal form method and center manifold theory. Finally, we show that the plankton system undergoes a transcritial bifurcation, and the equilibrium is unstable.