Permanence of species in nonautonomous discrete Lotka-Volterra competitive system with delays and feedback controls

A nonautonomous N-species discrete Lotka-Volterra competitive system of difference equations with delays and feedback controls is considered. New sufficient conditions are obtained for the permanence of this discrete system. The results indicate that one can choose suitable controls to make the species coexistence in the long run. Moreover, we give some examples to illustrate the feasibility of our result which can be well suited for computational purposes. (C) 2006 Elsevier B.V. All rights reserved.