On Diffusive Population Models with Toxicants and Time Delays

Abstract

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. © 1999 Academic Press.