Skip Navigation


IMA Journal of Applied Mathematics Advance Access originally published online on January 8, 2009
IMA Journal of Applied Mathematics 2009 74(2):296-323; doi:10.1093/imamat/hxn037
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
74/2/296    most recent
hxn037v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Zou, H.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Inhomogeneous spatial patterns for predator–prey models: bifurcation at a higher eigenvalue

Henghui Zou{dagger}

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA; Department of Mathematics Johns Hopkins University, Baltimore, MD 21218, USA

{dagger} Email: zou{at}math.uab.edu

Received on February 18, 2008; Revision received September 25, 2008. Accepted on October 23, 2008

In this paper, we study a Rosenzweig–MacArthur predator–prey (steady-state) model with diffusion and subject to homogeneous Neumann boundary conditions. Namely, we consider the following system of elliptic equations:

Formula
where {Omega} sub Rn (n ≥ 2) is a bounded and smooth domain. We call a pair of smooth (say, C2({Omega})) functions u(x) and v(x) which are strictly positive and non-constant in the region {Omega} and satisfy the above system a spatially inhomogeneous pattern. Employing global bifurcation theory and exploring the global structure of the system, we obtain new existence results of spatially inhomogeneous patterns of large amplitude and global nature.

Keywords: bifurcation; existence; Neumann boundary data; predator–prey; spatial patterns.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.