Persistence of delayed cooperative models: Impulsive control method

Abstract

In this paper, the problem of impulsive control for persistence of N-species cooperative models with time-varying delays are studied. A method on impulsive control is introduced to delayed cooperative models and some sufficient conditions for the persistence of the addressed models are derived, which are easy to check in real problems. The results show that proper impulsive control strategy may contribute to the persistence of cooperative populations and maintain the balance of an ecosystem. Conversely, the undesired impulsive control such as impulsive harvesting too frequently or impulsive harvesting too drastically may destroy the persistence of populations and leads to the extinction of some species. In addition, some discussions and comparisons with the recent works in the literature are given. Finally, the proposed method is applied to two numerical examples to show the effectiveness and advantages of our results.