Asymptotic behavior of the reaction–diffusion model of plankton allelopathy with nonlocal delays

In this paper, we consider a reaction–diffusion model of plankton allelopathy with nonlocal delays. Using an iterative technique, the global stability of the positive steady state and the semi-trivial steady states of the system is investigated under some weaker conditions than those assumed in Tian et al. [C.R. Tian, L. Zhang and Z. Ling, The stability of a diffusion model of plankton allelopathy with atio-temporal delays, Nonlinear Anal. RWA 10 (2009) 2036–2046]. We also show that toxic substances and nonlocal delays are harmless for the stability of the positive steady state. Finally, some examples are presented to verify our main results.