Extinction in nonautonomous Lotka–Volterra competitive system with pure-delays and feedback controls

In this paper, the extinction of species for general nn-species nonautonomous Lotka–Volterra competitive system with pure-delays and feedback controls is studied. New sufficient conditions of which a part of the nn species is driven to extinction are established by using the method of multiple Lyapunov functionals and by developing a new analysis technique. The numerical simulation shows that in a competitive system by introducing proper feedback controls we can make an extinct species become permanent.