Permanence, extinction and global attractivity of the periodic Gilpin–Ayala competition system with impulses

In this paper, a periodic nn-species Gilpin–Ayala competition system with impulses is studied. By constructing a suitable Lyapunov function and using the comparison theorem of impulsive differential equations, a set of sufficient conditions which guarantee that some species in the system are permanent and globally attractive while the remaining species are driven to extinction are obtained. Our results show that the dynamic behaviors of the system we considered are quite different from the corresponding system without impulses.