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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 454209, 8 pages
http://dx.doi.org/10.1155/2013/454209
Research Article

Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth

School of Electronic and Information Engineering, Gansu Lianhe University, Lanzhou 730000, China

Received 3 February 2013; Accepted 4 March 2013

Academic Editor: Yonghui Xia

Copyright © 2013 Bo Yang. 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

The spatiotemporal dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition are investigated analytically and numerically. The asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation around the positive equilibrium are shown; the conditions of Turing instability are obtained. And with the help of numerical simulations, it is found that the model exhibits complex pattern replication: stripes, spots-stripes mixtures, and spots Turing patterns.