Uniform persistence and global attractivity for nonautonomous competitive systems with nonlinear dispersion and delays

Abstract

In this paper, we consider a nonautonomous Lotka–Volterra competitive system with nonlinear discrete dispersion and a finite number of discrete delays. The system, which is consisted of two Lotka–Volterra patches, has two competitors: one can disperse between two patches, but the other is confined to one patch and cannot disperse. Our main focus is persistence, i.e. the survival in two patches of the population, and the existence of a periodic solution. We also establish conditions under which the system admits a positive periodic solution which attracts all solutions.