具有时滞和脉冲捕获、污染物脉冲输入的捕食-食饵-环境模型  

A Delayed Predator-prey-environment Model with Impulsive Harvesting and Pulse Input of Pollutant

作　　者：章培军[1] 王震[1] 陈恒[1] ZHANG Pei-jun;WANG Zhen;CHEN Heng(School of Science,Xijing University,Xi'an 710123)

机构地区：[1]西京学院理学院,西安710123

出　　处：《工程数学学报》2020年第6期731-741,共11页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11726624,61473237);陕西省教育厅科学研究计划项目(19JK0906);陕西省重点研发计划项目(2018GY-091);陕西省自然科学基础研究计划项目(2020JM-646,2016JM1024);陕西省复杂系统控制与智能信息处理重点实验室开放课题(2016CP06).

摘　　要：本文建立了污染环境中,捕食者具有阶段结构、食饵具有脉冲收获、污染物具有脉冲输入的时滞捕食-食饵-环境模型,利用离散动力系统的频闪映射和比较原理,得到了捕食者灭绝周期解的全局吸引性和系统持久性的充分条件.通过数值仿真,研究了食饵的捕获、污染物的脉冲输入和脉冲作用周期对捕食者灭绝和持续生存的影响,同时也验证了理论结果.对生物资源的开发、种群数量的收获及环境的控制提供了宝贵的理论依据.Established in this paper is a time-delay predator-prey-environment model with stage structure of predator,impulsive harvesting of prey and impulsive input of pollutant in polluted environment.By using the stroboscopic mapping and the comparison principle of discrete dynamical systems,sufficient conditions for the global attractiveness of the predator extinction periodic solution and system persistence are obtained.Through numerical simulation,the effects of the prey capture,pulse input of pollutants and pulse action period on the extinction and survival of predators are studied,and the theoretical results are verified.It provides valuable theoretical basis for the development of biological resources,the harvest of population number and the control of environment.

关 键 词：脉冲捕获 阶段结构 污染物脉冲输入 捕食-食饵-环境模型 灭绝周期解 持久性 

分 类 号：O175[理学—数学] Q141[理学—基础数学]