三种群捕食-竞争-合作混杂模型的全局渐近稳定性  

Global Asymptotic Stability of Predator-Competition-Cooperative Hybrid Population Models of Three Species

作　　者：郑涛[1] 周欣然 张龙[1] ZHENG Tao;ZHOU Xinran;ZHANG Long(College of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830046, China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《广西师范大学学报（自然科学版）》2020年第5期64-70,共7页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11861065,11771373,11702237);新疆教育厅重点实验室项目(2016D03022);新疆普通高等学校科研计划-创新团队项目(XJEDU2017T001);新疆大学博士创新项目(XJUBSCX-2017005)。

摘　　要：本文建立了一类三种群具有捕食-竞争-合作混杂交互关系的生态模型。首先引入辅助系统,应用微分方程比较原理,构造合适的Lyapunov函数以及分析方法,讨论了系统解的正性和有界性,建立正平衡点全局渐近稳定性的充分条件。然后通过数值模拟检验本文结论的有效性。This paper establishes a class of ecological model of three species with predator-competition-cooperative hybrid interaction.Firstly,the positivity and boundedness of the solution of the system are discussed by introducing auxiliary system and differential comparison principle.Next,the sufficient conditions of globally asymptotically stable positive equilibrium are abtained by constructing suitable Lyapunov functions and some analytical skills.Finally,numerical simulations are conducted to verify the theoretical results.

关 键 词：周期性 LYAPUNOV函数 全局渐近稳定性 捕食-竞争-合作混杂系统 

分 类 号：O175[理学—数学]