Some new results on the permanence and extinction of nonautonomous Gilpin–Ayala type competition model with delays

In this paper, we consider a delayed nonautonomous n  -species Gilpin–Ayala type competitive system, which is more general and more realistic then classical Lotka–Volterra type competition model. For each r⩽nr⩽n, we establish a series of criteria under which r   of the species in the system are permanent while the remaining n-rn-r species are driven to extinction.