Population dynamics in closed polluted aquatic ecosystems with time-periodic input of toxicants

Abstract

This paper is concerned with a diffusive population-toxicant system in a polluted aquatic environment with temporally periodic and spatially heterogeneous input of toxicants. By a variety of mathematical tools, such as the principal eigenvalue theory, method of upper-lower solutions, theory of monotone semi-flow, implicit function theorem, etc., we derive sufficient conditions on the existence and global stability of periodic solutions with fixed diffusion rates and explore the asymptotic profiles of positive periodic solutions for large and small diffusion rates. Our results show that if the toxicity of toxicants is low (resp. high), then the aquatic population persists (resp. becomes extinct), while both persistence and extinction may be locally stable (i.e. bi-stability) for moderate toxicity of toxicants. We also find that the spatial distribution of positive periodic solutions with small diffusion rates is quite different from that with large diffusion rates.