Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-I: The Case in
1 Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
2 Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Boundary Value Problems 2009, 2009:378763 doi:10.1155/2009/378763Published: 27 September 2009
This paper deals with a Holling type III diffusive predator-prey model with stage structure and nonlinear density restriction in the space . 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.