A diffusive toxin producing phytoplankton model with maturation delay and three-dimensional patch

The dynamics of a diffusive toxin producing phytoplankton model with maturation delay and three-dimensional patch subject to Neumann boundary condition is investigated in this paper. The global stability of boundary equilibrium is obtained. The local stability of the coexistent equilibrium and the existence of Hopf bifurcation are investigated. The conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived.