Abstract: This paper is concerned with a two-species competitive system of plankton allelopathy with delay. A modified differential equation model of plankton allelopathy having stimulatory effects on each other is investigated in this paper. By regarding the delay τ as the bifurcation parameter, firstly, the stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out for illustrating the theoretical results
