Abstract
In this paper, a system consisting of two harmful phytoplanktons and one zooplankton with two time delays is investigated. Firstly, the global existence, nonnegativity and boundedness of the solutions of the system are discussed. Secondly, using time delays as bifurcating parameters, the existence of local Hopf bifurcations at the positive equilibrium of the system is investigated in details. The phenomenon of stability switches is confirmed under some certain conditions. It is shown by numerical simulations under some suitable parameters that the system can exhibit complicated dynamic properties, and undergoes changes from stable periodic solution or equilibrium to chaos or from chaos to stable periodic solution or equilibrium. At last, some conclusions are given. The direction of the Hopf bifurcations and the stability of the bifurcation periodic solutions are given in Appendix by using the center manifold and normal form theory.
