环境污染中具有脉冲效应的捕食系统动力学分析  

Dynamic Analysis of the Predator-Prey System in a Polluted Environment with Impulsive

作　　者：刘娟[1] 胡杰 赵清[3] 李富忠 LIU Juan;HU Jie;ZHAO Qing(College of Arts and Sciences,Shanxi Agricultural University,Taigu 030801,China;School of software,Shanxi Agricultural University,Taigu 030801,China;College of Agriculture,Shanxi Agricultural University,Taigu 030801,China)

机构地区：[1]山西农业大学文理学院,山西太谷030801 [2]山西农业大学软件学院,山西太谷030801 [3]山西农业大学农学院,山西太谷030801

出　　处：《数学的实践与认识》2019年第22期294-298,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金面上项目(31872336);国家自然科学基金(31501876);山西省科技厅面上青年基金项目(201601D021122);山西农业大学科技创新基金项目(2017005,2017019)

摘　　要：针对环境问题日益严峻,考虑到种群密度制约项的影响,建立了环境污染中脉冲输入污染物,且具有HollingⅡ型的两种群捕食与被捕食系统的动力学模型.利用脉冲微分方程的积分均值法和比较定理,得到系统弱平均持续生存和种群灭绝的充分条件.理论可用来保护物种,尤其是濒临灭绝的物种,防止灭绝.We establish the predator-prey system with Holling Ⅱ functional response and impulsive effect in a polluted environment on increasingly serious environmental problems.The comparison techniques and integral mean method is employed to obtain the conditions for population extinction and weak average persistent of system to save the species.This theory can be used to protect species,especially endangered species,from extinction.

关 键 词：环境污染 脉冲作用 弱平均持续生存 灭绝 

分 类 号：O17[理学—数学]