Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-I: The Case in Rn | Hindawi Publishing Corporation Boundary Value Problems Volume 2009 Article ID 378763 26 pages doi 2009 378763 Research Article Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-I The Case in R Rui Zhang 1 Ling Guo 2 and Shengmao Fu2 1 Department of Mathematics Lanzhou Jiaotong University Lanzhou 730070 China 2 Department of Mathematics Northwest Normal University Lanzhou 730070 China Correspondence should be addressed to Shengmao Fu fusm@ Received 2 April 2009 Accepted 31 August 2009 Recommended by Wenming Zou This paper deals with a Holling type III diffusive predator-prey model with stage structure and nonlinear density restriction in the space R . 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 reactiondiffusion 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. 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. 1. Introduction Population models with stage structure have been investigated by many researchers and various methods and techniques have been used to study the existence and qualitative properties of solutions 1-9 . However most of the discussions in these works are devoted to either systems of ODE or weakly coupled systems of reaction-diffusion equations. In this paper we investigate the global existence and convergence of solutions for a strongly coupled cross-diffusion predator-prey model with stage structure and nonlinear density restriction. Nonlinear problems of this kind are quite
