Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (5): 653-664 .doi: https://doi.org/10.1007/s10483-008-0509-x

• Articles • 上一篇    下一篇

连续收获捕食者与脉冲存放食饵的阶段结构捕食-食饵模型的全局吸引和一致持久

焦建军, 陈兰荪, Juan J. Nieto, Torres Angela   

  1. 1.贵州财经学院数学与统计学院,贵阳 550004;
    2.大连理工大学应用数学系,辽宁 大连 116024;
    3.圣地亚哥-德孔波斯特拉大学数学分析系,15782 圣地亚哥-德孔波斯特拉,西班牙;
    4.圣地亚哥-德孔波斯特拉大学医学院精神、放射和公众健康系,15782 圣地亚哥-德孔波斯特拉,西班牙
  • 收稿日期:2007-07-30 修回日期:2008-03-18 出版日期:2008-05-18 发布日期:2008-05-18
  • 通讯作者: 焦建军

Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey

JIAO Jian-jun, CHEN Lan-sun, Juan J. Nieto, Torres Angela   

    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
  • Received:2007-07-30 Revised:2008-03-18 Online:2008-05-18 Published:2008-05-18
  • Contact: JIAO Jian-jun

摘要: 研究了一个捕食者具连续收获与食饵具脉冲存放的阶段结构时滞捕食-食饵模型。根据生物资源管理的实际,改进了捕食者具阶段结构的捕食-食饵模型,即原来假设每个捕食者个体都具有相同的捕食食饵的能力。假设捕食者按年龄分为两个阶段,即幼体和成体,而且幼体无能力捕食食饵。得到了捕食者灭绝周期解全局吸引和系统持久的充分条件。结论说明了脉冲存放食饵对系统的持久起了重要的作用,并且为生物资源管理提供了策略基础。数值分析也进一步说明了系统的动力学性质。

Abstract: We investigate a stage-structured delayed predator-prey model with impulsive 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 important 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.

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