A Stage-structured Predator-prey Model with Time Delay and Impulsive Effects  

作　　者：DU Yan-ke Wu Xiang-dong Xu Rui 

机构地区：[1]Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003,China [2]Department of Guns Engineering, Shijiazhuang Mechanical Engineering College, Shijiazhuang050003, China

出　　处：《Chinese Quarterly Journal of Mathematics》2014年第1期45-54,共10页数学季刊（英文版）

基　　金：Foundation item： Supported by the NNSF of China（11071254）; Supported by the Science Foundation of Mechanical Engineering College（YJJXMll004）

摘　　要：A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated, in which both the prey and the predator have a history that takes them through two stages： immature and mature. The global attractiveness of the pest-eradication periodic solution is discussed, and sufficient condition is obtained for the permanence of the system. Further, numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.

关 键 词：STAGE-STRUCTURE DELAY biological and chemical control impulsive effect global attractiveness PERMANENCE 

分 类 号：O175.1[理学—数学]