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Asymptotic behaviour of positive steady states to a predator—prey model

Published online by Cambridge University Press:  12 July 2007

Yihong Du
Affiliation:
School of Mathematics, Statistics and Computer Science, University of New England, Armidale, NSW 2351, Australia, and Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165, People's Republic of China (ydu@turing.une.edu.au)
Mingxin Wang
Affiliation:
Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, People's Republic of China, and Department of Mathematics,Southeast University, Nanjing 210018, People's Republic of China (mxwang@seu.edu.cn)

Abstract

To understand the heterogeneous spatial effect on predator–prey models, we study the behaviour of the positive steady states of a predator–prey model as certain parameters are small or large. We compare the case when the model has a spatial degeneracy with the case when it does not have such a degeneracy. Our results show that the effect of the degeneracy can be clearly observed in one limiting case, but not in the others.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2006

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