Global Stability of Almost Periodic Solution of a Discrete Multispecies Gilpin-Ayala Mutualism System

This paper discusses a discrete multispecies Gilpin-Ayala mutualism system. We first study the permanence and global attractivity of the system. Assume that the coefficients in the system are almost periodic sequences, we obtain the sufficient conditions for the existence of a unique almost periodic solution which is globally attractive and uniformly asymptotically stable by constructing a suitable Liapunov function, respectively. Two examples together with numerical simulation indicate the feasibility of the main results.