Boundary Value Problems
Volume 2009 (2009), Article ID 654539, 19 pages
doi:10.1155/2009/654539
Research Article

Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-II: The Case in ℝ1

Rui Zhang,1,2 Ling Guo,1 and Shengmao Fu1

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 2 April 2009; Accepted 31 August 2009

Academic Editor: Wenming Zou

Copyright © 2009 Rui Zhang et al. 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

A Holling type III predator-prey model with self- and cross-population pressure is considered. Using the energy estimate and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions to the model are dicussed. In addition, global asymptotic stability of the positive equilibrium point for the model is proved by Lyapunov function.