一类具有时滞和不育控制的单种群模型  

A model of single-specie with time lag and contraception control

作　　者：李秋英 LI Qiu-ying(School of Mathematics and Statistics,Huanghuai University,Zhumadian 463000,China)

机构地区：[1]黄淮学院数学与统计学院,河南驻马店463000

出　　处：《兰州理工大学学报》2022年第4期152-156,共5页Journal of Lanzhou University of Technology

基　　金：河南省科技攻关项目(182102110292),河南省高等学校重点科研项目(19B110009,20B110008)。

摘　　要：以生态安全为基础,不育技术比药物灭杀更能持久彻底地控制鼠类数量,已逐渐成为鼠害防控的发展方向.结合不育剂的有效期,建立了一类不育控制下的单种群模型,讨论了平衡点存在的条件,得到了种群零平衡点全局渐近稳定的充要条件和正平衡点全局渐近稳定的充分条件;分析了不育控制及药物的有效期对种群动态的影响.Based on ecological security,sterile technology has gradually become the development direction of rodent control,which can control rodent population more permanently and thoroughly than poison.Combined with the valid period of sterilant,a single-species population under sterility control is established.After the discussion of the conditions for the existence of equilibrium points,the necessary and sufficient conditions are obtained for guaranteeing global asymptotic stability of the zero equilibrium points,and the sufficient condition is obtained for guaranteeing global asymptotic stability of the positive equilibrium point.In the end,the effects of contraception control and the valid period of sterilant on the dynamics of the pest population are analyzed.

关 键 词：不育控制 平衡点 全局渐近稳定 

分 类 号：O175.13[理学—数学]