Oscillation and global attractivity in a periodic Nicholsonʹs blowflies model

In this paper, we shall consider the nonlinear delay differential equation N′(t) = −δ(t)N(t) + P(t)N(t − mω)e−aN(t−mω, where m is a positive integer, δ(t) and P(t) are positive periodic functions of period ω. In the nondelay case, we shall show that (∗) has a unique positive periodic solution N(t), and provide sufficient conditions for the global attractivity of N(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (∗) about N(t), and establish sufficient conditions for the global attractivity of N(t).