A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system is bistable(in the absence of feedback controls),then by choosing some suitable values of feedback control variables,one of the species is driven to extinction while the other one becomes globally stable.Examples together with their numerical simulations are presented to verify the feasibility of our results.Our results not only improve but also complement those of Z.Li,M.A.Han and F.D.Chen[Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,Nonlinear Anal.:Real World Appl.,14(2013),402-413].
