Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations

In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results.