Persistence for a class of nonautonomous systems of differential equations with unbounded delays

For a family of nonautonomous systems of differential equations with unbounded delays, sufficient conditions for their persistence are established. In general, these systems are non-cooperative, so the usual techniques for monotone systems do not apply. The class of differential equations studied here is broad enough to encompass important models with unbounded delays used in mathematical biology. Our results extend and improve recent criteria for persistence of systems of differential equations with finite delays, and are illustrated with some selected examples given here.