Permanence and global attractivity of the discrete Gilpin–Ayala type population model

Abstract

In this paper, we propose a discrete Gilpin–Ayala competition model and a discrete Gilpin–Ayala type multispecies competition–predator model. For general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained; For periodic case, sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained. An example together with its numeric simulations shows the feasibility of the main results.