Stability and bifurcation in a two harmful phytoplankton–zooplankton system

In this paper, a mathematical model consisting of two harmful phytoplankton and zooplankton with discrete time delays is considered. We prove that a sequence of Hopf bifurcations occur at the interior equilibrium as the delay increases. Meanwhile, the phenomenon of stability switches is found under certain conditions. The direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are determined by using the theory of normal form and center manifold. Numerical simulations are given to support the theoretical results.