Boundary Value Problems
Volume 2009 (2009), Article ID 654539, 19 pages
doi:10.1155/2009/654539
Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-II: The Case in ℝ1
Rui Zhang
, Ling Guo
and Shengmao Fu
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
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.