Permanence and partial extinction in an impulsive delay competitive system with the effect of toxic substances

In this paper we propose a periodic impulsive delay two-species competitive system in which two species have toxic inhibitory effects on each other. It is assumed that the system is impulsively controlled by means of harvesting and stocking controls. By using the theory of impulsive differential equation and analysis techniques, a set of sufficient conditions are derived for the permanence and partial extinction of the system. It turns out that the impulsive controls play a crucial role in shaping the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.