Existence and attractivity of a periodic solution for an NN-species Gilpin–Ayala impulsive competition system

In this paper, by using a comparison theorem, the method of coincidence degree and by constructing a suitable Lyapunov functional, we study the persistence, existence and attractivity of a periodic solution for an NN-species Gilpin–Ayala impulsive competition system. A set of sufficient conditions is obtained for the existence and global attractivity of a unique positive periodic solution of the model. Our new results improve and generalize former results. Examples show the feasibility of our main results.