The stability of a diffusion model of plankton allelopathy with spatio–temporal delays

A reaction–diffusion system with non-local delay is proposed to describe two competitive planktonic growths in aquatic ecology. The local and global stability of the axial equilibria as well as the positive equilibrium are discussed. Our results show that the delay has no effect on the stability of the axial equilibria; on the other hand, the positive equilibrium can be induced to be locally unstable by the delay. Finally, the corresponding numerical simulations are also demonstrated.