Global attractivity in delayed differential equations with applications to “food-limited” population model

A new criterion is built, which guarantees the global attractivity of zero solution for equation having the form x′(t)=(1+x(t))F(t,xt). The behavior of global solution on R is also addressed. As an application, we study the existence of globally attractive positive almost periodic solution for the “food-limited” single population model. Our results improve those in literature.