Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 54861, 15 pages
doi:10.1155/2007/54861
Permanence and stability of an age-structured prey-predator system with delays
Liming Cai1
, Xuezhi Li1
, Xinyu Song1
and Jingyuan Yu4
1College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, China
4Beijing Institutes of Information and Control, Beijing 100037, China
Abstract
An age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, sufficient conditions are also obtained for the global asymptotic stability of the positive equilibrium of the model.