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IMA Journal of Applied Mathematics Advance Access published online on June 23, 2008
IMA Journal of Applied Mathematics, doi:10.1093/imamat/hxn016
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Sharp spatial patterns of the diffusive Holling–Tanner prey–predator model in heterogeneous environment

Mingxin Wang{dagger}

Department of Mathematics, Southeast University, Nanjing 210018, People's Republic of China and Department of Mathematics, Xuzhou Normal University, Xuzhou 221116, People's Republic of China

Peter Y. H. Pang{ddagger}

Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543

Wenyan Chen

Department of Mathematics, Southeast University, Nanjing 210018,People's Republic of China

{dagger} Email: mxwang{at}seu.edu.cn

{ddagger} Corresponding author. Email: matpyh{at}nus.edu.sg

Received on May 22, 2007; Accepted on April 9, 2008

This paper studies positive steady-state solutions of the diffusive Holling–Tanner prey–predator model in heterogeneous environments subject to the homogeneous Neumann boundary condition. In particular, it investigates the appearance of sharp spatial patterns arising from degeneracies of the model.

Keywords: Holling–Tanner prey–predator model; heterogeneous environments; diffusion; positive steady states; spatial patterns.


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