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This paper is concerned with the classical Nicholson-Bailey model (15) defined by fλ(x, y )=( y(1  ex) ,λ yex). We show that for λ = 1 a heteroclinic foliation exists and for λ> 1 global strict oscillations take place. The important phenomenon of delay of stability loss is established for a general class of discrete dynamical systems, and it is applied to the study of nonexistence of periodic orbits for the Nicholson-Bailey model.

Heteroclinic foliation, global oscillations for the Nicholson-Bailey model and delay of stability loss