On diffusive population models with toxicants and time delays

In this article we study the global stability in reaction-diffusion models for single-species population growth under environmental toxicants with or without time delays. The existence and uniqueness of a positive steady-state solution are established in those models. It is shown that as long as the magnitude of the instantaneous self-limitation and toxicant effects is larger than that of the time-delay effects in the model with delays, the solution of both reaction-diffusion systems has the same asymptotic behavior (extinction or converging to the positive steady-state solution, depending on the growth rate of the species). Numerical simulations for both cases (with or without time delays) are demonstrated for the purpose of comparison. (C) 1999 Academic Press.