1School of Mathematical and Computer Sciences, University of New England, Armidale, NSW 2351, Australia
2Department of Mathematics, Ohio State University, Columbus, OH 43214, USA
Tóm tắt
We study a predator–prey system with Holling–Tanner interaction terms. We show 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 estimates on the ranges of other parameters where spatially inhomogeneous solutions can exist. We also determine the asymptotic behaviour of the spatially inhomogeneous solutions as m → ∞, and an interesting relation between this population model and free boundary problems is revealed.
