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|Title:||Quantitative analysis of a prey-predator model with stage structure for the predator||Contributor(s):||Du, Yihong (author) ; Pang, Peter Y H (author); Wang, Mingxin (author)||Publication Date:||2008||DOI:||10.1137/070684173||Handle Link:||https://hdl.handle.net/1959.11/3690||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||Statistics to Oct 2018:||Visitors: 215|
|Appears in Collections:||Journal Article|
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