Boundary Value Problems
Volume 2009 (2009), Article ID 378763, 26 pages
doi:10.1155/2009/378763
Research Article

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

Rui Zhang,1 Ling Guo,2 and Shengmao Fu2

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

This paper deals with a Holling type III diffusive predator-prey model with stage structure and nonlinear density restriction in the space ℝn. We first consider the asymptotical stability of equilibrium points for the model of ODE type. Then, the existence and uniform boundedness of global solutions and stability of the equilibrium points for the model of weakly coupled reaction-diffusion type are discussed. Finally, the global existence and the convergence of solutions for the model of cross-diffusion type are investigated when the space dimension is less than 6.