Global Stability of Almost Periodic Solution of a Discrete Multispecies Gilpin-Ayala Mutualism System
Hui Zhang *
Mathematics and OR Section, Xi’an Research Institute of High-tech Hongqing Town, Xi’an, Shaanxi 710025, China
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Almost periodic solution, discrete, gilpin-ayala mutualism system, permanence, global attractivity, uniformly asymptotically stable