Nonlinear models for the effect of pollutants on population with time delay

Abstract

AbstractIn this paper, a mathematical model is proposed and analysed to study the effect of pollution on a population, which is living in an environment polluted by its own activities with time delay in a diffusive system. It has been assumed that the pollutants enter into the environment not directly by the population but by a precursor produced by the population itself. It has been further assumed that the larger the population, the faster the precursor is produced, and the larger the precursor, the faster the pollutant is produced. In the absence of diffusion, criteria for local stability, instability and global stability are obtained. The effect of diffusion on the positive equilibrium of the system is also investigated. Some investigations have been made in recent decades [1, 2, 3]. But, the effect of Diffusion has not been considered in the above investigations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)