具有脉冲效应的Holling-Tanner捕食-被捕食系统的正周期解  

Existence of Positive Periodic Solution of the Holling-Tanner Predator-Prey System with Impulsive Effect

作　　者：杨晓峰[1] 靳祯[1] 孙桂全[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《测试技术学报》2010年第3期225-230,共6页Journal of Test and Measurement Technology

基　　金：国家自然科学基金资助项目(10471040);教育部新世纪人才资助计划项目NCET050271);山西省自然科学基金资助项目(2009011005-1)

摘　　要：为了描述突然性因素对捕食-被捕食系统的影响,本文建立了具有固定时刻脉冲影响的Holling-Tanner捕食-被捕食系统模型,研究了系统的正周期解的存在性.利用基于叠合度理论的连续定理,证明了模型的正T-周期解的存在性,给出了系统存在正周期解的条件,该条件由两个种群的内禀增长率、脉冲周期及一个脉冲周期内的脉冲影响总量给出,这说明脉冲影响可能导致种群系统的平衡状态发生改变.A model with impulsive effects at some given moments for Holling-tanner predator-prey system is constructed to describe the effect of some abrupt incidents. The existence of positive periodic solution of the system is studied. By the continuous theorem from coincidence degree theory, it is showed that the system has a positive periodic solution with the period T under some conditions. They are formulated by intrinsic growth rate, impulsive period, amount of impulsive effect within an impulsive period of the two populations. This conclusion shows that the balance of the system can be changed by impulsive effects.

关 键 词：脉冲效应 Holling—Tanner捕食-被捕食系统 周期解 叠合度 脉冲微分方程 

分 类 号：O175.14[理学—数学] O177.92[理学—基础数学]