Permanence of a delayed non-autonomous Gilpin–Ayala competition model

In this paper, we consider a delayed non-autonomous n-species Gilpin–Ayala competitive system, which is more general and more realistic then classical Lotka–Volterra competition model. By means of Ahmad and Lazer’s definitions of lower and upper averages of a function, we give the average conditions for the permanence of the system. It is shown that our result is the generalization of those of Zhao et al. [J.D. Zhao, J.F. Jiang, A.C. Lazer, The permanence and global attractivity in a nonautonomous Lotka–Volterra system, Nonlinear Analysis: Real World Applications, 5 (4) (2004), 265–276]. Our results also supplement the results of Fan and Wang [M. Fan, K. Wang, Global periodic solutions of a generalized n-species Gilpin–Ayala competition model, Computer and Mathematics with Applications, 40 (2000), 1141–1151].