一类具有避难所和时滞的非自治阶段结构捕食系统的动力学分析  

Dynamical Analyses of a Nonautonomous Prey-predator Stage Structure System with Refuges and Time Delay

作　　者：宋鸽 甘静雯 SONG Ge;GAN Jingwen(College of Information and Management Science,Henan Agricultural University,Zhengzhou 450002,China;College of Veterinary Medicine,Henan Agricultural University,Zhengzhou 450002,China;College of Forestry,Henan Agricultural University,Zhengzhou 450002,China)

机构地区：[1]河南农业大学信息与管理科学学院,河南郑州450002 [2]河南农业大学动物医学院,河南郑州450002 [3]河南农业大学林学院,河南郑州450002

出　　处：《信阳师范学院学报（自然科学版）》2024年第2期203-209,共7页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12001417);河南农业大学博士启动基金项目(30501166;30501170)。

摘　　要：研究了一类具有阶段结构的捕食者与具有避难所的两类竞争性食饵的捕食系统。利用比较定理,得到了系统一致持久的充分条件。根据Leray-Schauder不动点定理以及构造合适的Lyapunov函数,得到了系统正周期解的存在性和全局渐近稳定性的充分条件。结果表明,增加避难所数量并提高其对食饵的庇护能力,可以增加食饵的种群密度,有效防止捕食者种群数量急剧下降,从而实现三者共存,进而达到保护物种多样性、维护生态系统平衡的目的。A predator-prey system with stage structure and two-competitive-prey with refuges was studied.By comparative theorems,sufficient conditions for permanence of the system were obtained.The sufficient conditions for the existence and global asymptotic stability of positive periodic solutions were derived through Leray-Schauder theorem and constructing appropriate Lyapunov function.The results showed that increasing the number of refuges and enhancing their sheltering capacity could increase the population density of prey,which would effectively prevent a sharp decline in predator population,thereby achieve the coexistence among three species and ultimately prompt species diversity conservation and maintain ecosystem balance.

关 键 词：避难所 时滞 阶段结构 非自治捕食系统 持久性 全局渐近稳定 

分 类 号：O175[理学—数学]