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

Published online by Cambridge University Press:  11 July 2007

Yihong Du  and
Yuan Lou
Yihong Du
Affiliation:
School of Mathematical and Computer Sciences, University of New England, Armidale, NSW 2351, Australia
Yuan Lou
Affiliation:
Department of Mathematics, Ohio State University, Columbus, OH 43214, USA
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Abstract

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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 2 , April 2001 , pp. 321 - 349
Copyright
Copyright © Royal Society of Edinburgh 2001

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