Global exponential stability of positive periodic solution of the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays

Abstract

ABSTRACTIn this paper, we study the n-species impulsive Gilpin–Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.