Boundary Value Problems
Volume 2010 (2010), Article ID 285961, 24 pages
doi:10.1155/2010/285961
Research Article

Global Existence and Convergence of Solutions to a Cross-Diffusion Cubic Predator-Prey System with Stage Structure for the Prey

Huaihuo Cao1 and Shengmao Fu2

1Department of Mathematics and Computer Science, Chizhou College, Chizhou 247000, China
2College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China

Received 3 December 2009; Accepted 30 March 2010

Academic Editor: Wenming Zou

Copyright © 2010 Huaihuo Cao and Shengmao Fu. 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

We study a cubic predator-prey system with stage structure for the prey. This system is a generalization of the two-species Lotka-Volterra predator-prey model. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the global existence of solutions and the stability of equilibrium points to the system of weakly coupled reaction-diffusion type are discussed. Finally, the existence of nonnegative classical global solutions to the system of strongly coupled reaction-diffusion type is investigated when the space dimension is less than 6, and the global asymptotic stability of unique positive equilibrium point of the system is proved by constructing Lyapunov functions.