Boundary Value Problems
Volume 2009 (2009), Article ID 378763, 26 pages
doi:10.1155/2009/378763
Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-I: The Case in ℝn
Rui Zhang1
, Ling Guo2
and Shengmao Fu2
1Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
2Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
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.