Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 267173, 9 pages
http://dx.doi.org/10.1155/2013/267173
Research Article

Qualitative Analysis of a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth

Zongmin Yue1 and Wenjuan Wang2

1Faculty of Science, Shaanxi University of Science and Technology, Xi’an 710021, China
2Department of Biostatistics and Computational Biology, University of Rochester Medical Center, 601 Elmwood Avenue, P.O. Box 630, Rochester, NY 14642, USA

Received 28 January 2013; Accepted 15 February 2013

Academic Editor: Yonghui Xia

Copyright © 2013 Zongmin Yue and Wenjuan Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigated the dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition. Some qualitative properties, including the dissipation, persistence, and local and global stability of positive constant solution, are discussed. Moreover, we give the refined a priori estimates of positive solutions and derive some results for the existence and nonexistence of nonconstant positive steady state.