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

Yihong Du; Mingxin Wang

doi:10.1017/S0308210500004704

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

Yihong Du, Mingxin Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

37 Citations (Scopus)

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.

Original language	English
Pages (from-to)	759-778
Journal	Proceedings of the Royal Society of Edinburgh. Section A: Mathematics
Volume	136A
DOIs	https://doi.org/10.1017/S0308210500004704
Publication status	Published - 2006

Keywords

Ordinary Differential Equations, Difference Equations and Dynamical Systems

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10.1017/S0308210500004704

https://hdl.handle.net/1959.11/3765

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title = "Asymptotic behaviour of positive steady states to a predator-prey model",

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.",

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AU - Du, Yihong

AU - Wang, Mingxin

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Ordinary Differential Equations, Difference Equations and Dynamical Systems

UR - https://www.scopus.com/pages/publications/33748289423

U2 - 10.1017/S0308210500004704

DO - 10.1017/S0308210500004704

M3 - Article

SN - 0308-2105

VL - 136A

SP - 759

EP - 778

JO - Proceedings of the Royal Society of Edinburgh. Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh. Section A: Mathematics

ER -

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

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