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Title: Quantitative analysis of a prey-predator model with stage structure for the predator
Contributor(s): Du, Yihong  (author)orcid ; Pang, Peter Y H (author); Wang, Mingxin (author)
Publication Date: 2008
DOI: 10.1137/070684173
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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.
Publication Type: Journal Article
Source of Publication: SIAM Journal on Applied Mathematics, 69(2), p. 596-620
Publisher: Society for Industrial and Applied Mathematics
Place of Publication: USA
ISSN: 0036-1399
Field of Research (FOR): 019999 Mathematical Sciences not elsewhere classified
Socio-Economic Objective (SEO): 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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