Dynamics of a Diffusive Predator–Prey Model: The Effect of Conversion Rate

Shanshan Chen; Junjie Wei; Jianhui Zhang

doi:10.1007/s10884-017-9618-y

Dynamics of a Diffusive Predator–Prey Model: The Effect of Conversion Rate

Shanshan Chen
, Junjie Wei^*
, Jianhui Zhang

^*Corresponding author for this work

Harbin Institute of Technology Weihai

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

6 Scopus citations

Abstract

A general diffusive predator–prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator–prey models and give some ranges of parameters where complex pattern formation cannot occur.

Original language	English
Pages (from-to)	1683-1701
Number of pages	19
Journal	Journal of Dynamics and Differential Equations
Volume	30
Issue number	4
DOIs	https://doi.org/10.1007/s10884-017-9618-y
State	Published - 1 Dec 2018
Externally published	Yes

Keywords

Global attractivity
Non-existence
Reaction–diffusion
Steady state

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10.1007/s10884-017-9618-y

Cite this

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title = "Dynamics of a Diffusive Predator–Prey Model: The Effect of Conversion Rate",

abstract = "A general diffusive predator–prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator–prey models and give some ranges of parameters where complex pattern formation cannot occur.",

keywords = "Global attractivity, Non-existence, Reaction–diffusion, Steady state",

author = "Shanshan Chen and Junjie Wei and Jianhui Zhang",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media, LLC.",

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T2 - The Effect of Conversion Rate

AU - Chen, Shanshan

AU - Wei, Junjie

AU - Zhang, Jianhui

PY - 2018/12/1

Y1 - 2018/12/1

N2 - A general diffusive predator–prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator–prey models and give some ranges of parameters where complex pattern formation cannot occur.

AB - A general diffusive predator–prey model is investigated in this paper. We prove the global attractivity of constant equilibria when the conversion rate is small, and the non-existence of non-constant positive steady states when the conversion rate is large. The results are applied to several predator–prey models and give some ranges of parameters where complex pattern formation cannot occur.

KW - Global attractivity

KW - Non-existence

KW - Reaction–diffusion

KW - Steady state

UR - https://www.scopus.com/pages/publications/85029171527

U2 - 10.1007/s10884-017-9618-y

DO - 10.1007/s10884-017-9618-y

M3 - 文章

AN - SCOPUS:85029171527

SN - 1040-7294

VL - 30

SP - 1683

EP - 1701

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 4

ER -

Dynamics of a Diffusive Predator–Prey Model: The Effect of Conversion Rate

Abstract

Keywords

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