Oscillation and global attractivity in a periodic Nicholson's blowflies model

In this paper, we shall consider the nonlinear delay differential equation N′(t) = -δ(t)N(t) + P(t)N(t - mw)e^{-aN(t - mw)}, (*) where tn is a positive integer, δ(t) and P(t) are positive periodic functions of period w. In the nondelay case, we shall show that (*) has a unique positive periodic solution N̄(t), and provide sufficient conditions for the global attractivity of N̄(t). In the delay case, we shall present sufficient conditions for the oscillation of all positive solutions of (*) about N̄(t), and establish sufficient conditions for the global attractivity of N̄(t).