具有收获率的HollingⅢ类捕食模型的定性分析  

Qualitative Analysis of Predator-Prey Model with Holling Ⅲ and Harvesting Rate

作　　者：张剑[1] 张宏民[1] 堵秀凤[1] 

机构地区：[1]齐齐哈尔大学理学院,黑龙江齐齐哈尔161006

出　　处：《哈尔滨理工大学学报》2011年第4期121-125,共5页Journal of Harbin University of Science and Technology

基　　金：黑龙江省自然科学基金资助项目(A201014);齐齐哈尔大学青年教师科研启动支持计划--科学技术类一般项目(2010k-M27);黑龙江省教育厅科学技术研究项目(12511610)

摘　　要：针对一类在食饵种群具有密度制约项条件下的具有线性收获率的HollingⅢ类功能性反应的捕食模型进行了定性分析.讨论了该模型各个平衡点在不同条件下的性态,绘制出模型的相轨线,根据轨线走向和定理验证平衡点的全局稳定性.通过构造Dulac函数得到了平衡点周围不存在闭轨线的条件.同时探讨了模型解的有界性,进而得到了模型的唯一正平衡点的全局稳定的充分条件.同时利用数值模拟的方法,对收获率及平衡点的稳定性的影响也进行了分析.In this paper,a predator-prey model with Holling Ⅲ functional response and linear harvesting rate is researched,in which the prey is under density restriction.The paper discusses the properties of every equilibrium under different conditions.By drawing the path curve,analyzing the directions of the curve and,the global equilibrium is verified.At the same time,by constructing Dulac function,the condition of surrounding of equilibrium without close path curve is obtained.The boundness of solutions and the sufficient conditions of positive equilibrium which is global are discussed.By using numerical simulation,it analyzes the influence of harvesting rate to the stability of equilibrium.

关 键 词：平衡点 收获率 全局稳定 数值模拟 

分 类 号：O175.13[理学—数学]