Appl. Math. Mech. -Engl. Ed., 2008, 29(5):653–663 DOI 10.1007/s10483-008-0509-x c Editorial Committee of Appl. Math. Mech. and Springer-Verlag 2008 Applied Mathematics and Mechanics (English Edition) Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey ∗ JIAO Jian-jun ( ) 1,2 , CHEN Lan-sun ( ) 2 , Juan J. Nieto 3 , Torres Angela 4 (1. School of Mathematics and Statistics, Guizhou College of Finance and Economics, Guiyang 550004, P. R. China; 2. Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China; 3. Department of Mathematical Analysis, Faculty of Mathematics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain; 4. Department of Psychiatry, Radiology and Public Health Faculty of Medicine University of Santiago de Compostela, Spain) (Communicated by GUO Xing-ming) Abstract We investigate a stage-structured delayed predator-prey model with impul- sive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an impor- tant role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system. Key words stage-structured, impulsive stocking, continuous harvesting, global attrac- tivity, permanence Chinese Library Classification O175 2000 Mathematics Subject Classification 34A37, 92B05 Introduction Impulsive differential equations are suitable for the mathematical simulation of the evolu- tionary process; its theory has obtained many good results [1−3] . The application of impulsive * Received Jul. 30, 2007 / Revised Mar. 18, 2008 Project supported by the National Natural Science Foundation of China (No. 10771179) and the Emphasis Subject of Guizhou Province of China Corresponding author JIAO Jian-jun, E-mail: jiaojianjun05@126.com