Oscillation in a discrete partial delay Nicholsonʹs Blowflies Model

In this paper, we shall consider the discrete partial delay Nicholsonʹs blowflies model where Pm,n represents the size of population at time m and site n, δ, a, and q are positive constants, and σ and τ are nonnegative integers. We prove that every positive solution of (∗) which does not oscillate about the positive equilibrium point P∗ converges to P∗ as m, n → ∞, and present some sufficient conditions for oscillation of all positive solutions about P∗.