Extinction in a nonautonomous Lotka–Volterra competitive system with infinite delay and feedback controls

In this paper, we propose a Lotka–Volterra competitive system with infinite delay and feedback controls. By using the method of multiple Lyapunov functionals and by developing a new analysis technique, we establish the sufficient conditions which guarantee that some of the nn species are driven to extinction. Two examples together with their numerical simulations show the feasibility of our main results and the considerable effects of feedback controls on the extinction of species.