Open Access 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

Author Affiliations

1 Department of Mathematics and Computer Science, Chizhou College, Chizhou 247000, China

2 College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, China

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Boundary Value Problems 2010, 2010:285961  doi:10.1155/2010/285961

Published: 18 May 2010

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.