具有庇护效应且捕食者有病的食饵-捕食者模型分析  

Analysis of The Prey-Predator Model with Sheltered Effect and Epidemic in Predator

作　　者：胡永亮 冯宇星 HU Yong-liang;FENG Yu-xing(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《兰州文理学院学报（自然科学版）》2018年第6期25-29,共5页Journal of Lanzhou University of Arts and Science(Natural Sciences)

摘　　要：建立并研究了捕食者具有传染病的食饵-捕食模型,该模型假设不仅健康的捕食者捕食食饵,染病的捕食者同样捕食食饵,只不过捕食能力要弱于健康的捕食者,还考虑了染病捕食者的恢复能力以及食饵的庇护能力,更加符合实际.证明了系统解的有界性,对系统的非负平衡点进行分析,并通过特征根法讨论了非负平衡点的局部稳定性.A predator-prey model of predator with infectious diseases is established and studied.The model assumes that not only healthy predator preys,but also infected predator preys.However,the infected predator’s predatory ability is weaker than that of healthy predator.The model also considers the recovery ability of infected predator and the shelter ability of prey.It is more realistic.The boundedness of the solution of the system is studied,the non-negative equilibrium point of the system is analyzed,and the local stability of the non-negative equilibrium point is discussed by the eigenvalue method.

关 键 词：食饵-捕食者 平衡点 渐近稳定性 传染病 

分 类 号：O175.1[理学—数学]