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Abstract and Applied Analysis
Volume 2011, Article ID 547060, 16 pages
http://dx.doi.org/10.1155/2011/547060
Research Article

Positive Solutions for a General Gause-Type Predator-Prey Model with Monotonic Functional Response

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 30 April 2011; Revised 12 June 2011; Accepted 20 June 2011

Academic Editor: Gabriella Tarantello

Copyright © 2011 Guohong Zhang and Xiaoli 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 study a general Gause-type predator-prey model with monotonic functional response under Dirichlet boundary condition. Necessary and sufficient conditions for the existence and nonexistence of positive solutions for this system are obtained by means of the fixed point index theory. In addition, the local and global bifurcations from a semitrivial state are also investigated on the basis of bifurcation theory. The results indicate diffusion, and functional response does help to create stationary pattern.