Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

Yihong Dua1 and Mingxin Wanga2

a1 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)

a2 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.

(Received July 12 2004)

(Accepted August 24 2005)