The effects of a single stage-structured population model with impulsive toxin input and time delays in a polluted environment

Abstract

Uncontrolled contribution of pollutant to the environment has led many species to extinction and several others are at the verge of extinction. This article deals with the dynamics of a single stage-structured population model with impulsive toxin input and time delays (including constant individual maturation time delay and pollution time delay) in a polluted environment, in which we assume that only the mature individuals are affected by pollutants. We obtain conditions for the global attractivity of the population-extinction periodic solution and the permanence of the population. We show that maturation time delay and impulsive toxin input can bring great effects on the dynamics of the system, and pollution time delay is harmless. Numerical simulations confirm our theoretical results.

Keywords:

• environmental pollution
• impulsive toxin input
• stage-structured
• time delay
• global attractivity

AMS Subject Classifications::

• 34D20
• 92D25

Acknowledgements

This work is supported by National Natural Science Foundation of China (10671001) and Science and Research Project Foundation of Liaoning Province Education Department.