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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  and
Mingxin Wang
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)
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Abstract

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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
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 4 , August 2006 , pp. 759 - 778
Copyright
Copyright © Royal Society of Edinburgh 2006