Permanence for nonautonomous Lotka–Volterra cooperative systems with delays

Abstract

In this paper, we consider a class of nonautonomous two species Lotka–Volterra cooperative population systems with time delays, and establish sufficient conditions which ensure the system to be permanent. We improve and extend the known condition of the permanence in [G. Lu and Z. Lu, Permanence for two species Lotka–Volterra cooperative systems with delays, Math. Biosci. Eng. 5 (2008) 477–484] to nonautonomous two-species Lotka–Volterra cooperative systems. Moreover, our conditions need no restriction on the size of time delays.