Copyright © 2013 Bing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Without any question, environmental pollution is the main cause
for the species extinction in recent times. In this paper, based
on impulsive differential equation, the dynamics of a
single-species model with impulsive pollution treatment at fixed
time in a polluted environment is considered, in which we assume
that the species is directly affected by the pollutants.
Sufficient conditions for permanence and extinction of the species
are given. The results show that the species is permanent when the
impulsive period is less than some critical value, otherwise the
species will be extinct. Although shortening the impulsive period
can protect the species from extinction, it is expensive. To see
how pollution treatment applications could be economical, we also
establish a hybrid impulsive model involving periodic pollution
treatment at fixed time with state-dependent pollution treatment
applied when the pollution concentration reaches the given
Environment Threshold (ET). It indicates that the hybrid method is
the most effective method to protect the species from extinction.
Numerical simulations confirm our theoretical results.