Quantitative analysis of a prey-predator model with stage structure for the predator

Title
Quantitative analysis of a prey-predator model with stage structure for the predator
Publication Date
2008
Author(s)
Du, Yihong
( author )
OrcID: https://orcid.org/0000-0002-1235-0636
Email: ydu@une.edu.au
UNE Id une-id:ydu
Pang, Peter Y H
Wang, Mingxin
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Society for Industrial and Applied Mathematics
Place of publication
United States of America
DOI
10.1137/070684173
UNE publication id
une:3781
Abstract
In this paper, we propose a diffusive prey-predator model with stage structure for the predator. We first analyze the stability of the nonnegative steady states for the reduced ODE system and then study the same question for the corresponding reaction-diffusion system with homogeneous Neumann boundary conditions. We find that a Hopf bifurcation occurs in the ODE system, but no Turing pattern happens in the reaction-diffusion system. However, when a natural cross diffusion term is included in the model, we can prove the emergence of stationary patterns (i.e., nonconstant positive stationary solutions) for this system; moreover, these stationary patterns do not exist in the considered parameter regime when there is no cross diffusion.
Link
Citation
SIAM Journal on Applied Mathematics, 69(2), p. 596-620
ISSN
1095-712X
0036-1399
Start page
596
End page
620

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