Extinction in a Lotka-Volterra competitive system with impulse and the effect of toxic substances

In this paper, an impulsive Lotka-Volterra competitive system with the effect of toxic substances is considered. By using some analytical technique, we prove that under certain conditions the species x2 of the system will be driven to extinction while the species x1 will be globally attractive with any positive solution of an impulsive Logistic equation. As a result, we extend the principle of competitive exclusion to a T-periodic competitive system with impulse and toxic substances. The main result in this paper is a good extension and supplement that of Li and Chen (2006). Furthermore, the obtained results supplement the results of Liu et al. (2009).