一类具有Holling-Ⅲ功能反应的捕食系统的脉冲控制  

Pulse Control to Predator-prey System with Holling-Ⅲ Functional Response

作　　者：刘雨林[1] 赵文才[1] 张同迁[1] 

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《山东科技大学学报（自然科学版）》2014年第2期86-95,共10页Journal of Shandong University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(11371230);山东省自然科学基金项目(ZR2012AM012);山东省高等学校科技计划项目(J13LI05)

摘　　要：建立了一类具有状态脉冲的Holling-Ⅲ类捕食系统模型,当捕食者的数量达到一定值时,人工收获捕食者,同时收获或添加食饵,使两者的综合收益达到最大。对无脉冲作用的系统进行定性分析,得到正平衡点存在且全局渐近稳定的条件。利用后继函数方法及脉冲微分方程几何理论,讨论状态脉冲控制下系统阶一周期解的存在性,并证明周期解是轨道渐近稳定的。最后,利用数值模拟进行验证,讨论系统的生态意义。A predator-prey system model with Holling-Ⅲ functional response and state dependent pulse control was formulated for the study. In order to get the maximum composite income, we captured predators and gathered or added prey in the same time when the number of predators reached a specified value. Through the qualitative analysis of the system without impulse effect,the sufficient condition for the existence and global stability of the positive equilibrium was obtained. Based on the successor function and impulsive differential geometry theory, the existence of order-one periodic solution of the system under state impulsive control was discussed. Besides,the orbit asymptotical stability of the periodic solution was proved through experiments. Lastly, to verify the theoretical results, some numerical sire ulations were given and the biological significance of the system was summarized.

关 键 词：Holling-Ⅲ类功能反应 状态脉冲 后继函数 阶一周期解 轨道渐近稳定 

分 类 号：O175[理学—数学]