Qualitative behaviour of positive solutions of a predator-prey model: effects of saturation

We study a predator-prey system with Holling-Tanner interaction terms. We s how that if the saturation rate m is large, spatially inhomogeneous steady- state solutions arise, contrasting sharply with the small-m case, where no such solution could exist. Furthermore, for large m, we give sharp estimate s on the ranges of other parameters where spatially inhomogeneous solutions can exist. We also determine the asymptotic behaviour of the spatially inh omogeneous solutions as m --> infinity, and an interesting relation between this population model and free boundary problems is revealed.