The Nicholson-Bailey model describes seasonal host-parasitoid interaction. Hosts surviving random attacks reproduce, while parasitoid offspring are proportional to attacked hosts. For , its positive equilibrium is , . Counting attacked rather than surviving hosts makes its predator reproduction law different from the annual pulse-breeding predator-prey model.
At the positive Nicholson-Bailey model equilibrium, lies between one and two, and the displayed determinant exceeds one. These follow from for . The discriminant is therefore negative, and the conjugate eigenvalues have moduli greater than one. Nearby annual samples spiral outward rather than approach coexistence.
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The Nicholson–Bailey model is a mathematical framework used in the field of ecology, particularly in the study of population dynamics. It is primarily concerned with understanding the interactions between predators and their prey, and it serves to explore how these interactions influence the populations of both species over time. The model was developed by the ecologists A.J. Nicholson and V.A. Bailey in the 1930s. It describes a system of two populations: one of predators and one of prey.