具有时滞和阶段结构的生态-流行病模型的稳定性及Hopf分支  

Stability and Hopf Bifurcation of an Eco-epidemiological Predator-prey Model with Stage-structure and Time Delay

作　　者：王玲书[1] 姚沛[2] WANG Ling-shu;YAO Pei(School of Mathematics and Statistics,Hebei University of Economics&Business,Shijiazhuang 050061;Department of International Trade Management,Shijiazhuang Information Engineering Vocational College,Shijiazhuang 050035)

机构地区：[1]河北经贸大学数学与统计学学院,石家庄050061 [2]石家庄信息工程职业学院国际贸易管理系,石家庄050035

出　　处：《工程数学学报》2018年第4期427-444,共18页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11371368);河北省教育厅科学技术研究项目(ZD2018052);河北经贸大学基金(2015KYQ01)~~

摘　　要：本文研究一类具有时滞和阶段结构的生态-流行病模型的稳定性及其Hopf分支.给出了边界平衡点和正平衡点存在的充分条件;通过分析特征方程,运用Hurwitz判定定理,讨论了边界平衡点和正平衡点的局部稳定性,并得到了正平衡点附近存在Hopf分支的充分条件;通过构造适当的Lyapunov泛函,运用LaSall不变集原理,讨论了边界平衡点和正平衡点的全局稳定性,从而得到了该生态模型永久持续生存与灭绝的充分条件.In this paper,the stability and Hopf bifurcation of an eco-epidemiological model with a time delay and a stage structure is investigated.By analyzing the characteristic equations and applying Hurwitz criterion,the local stability of the boundary equilibria and the positive equilibrium are discussed,respectively.Moreover,it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium.By using Lyapunov functions and LaSalle’s invariance principle,the global stability of the boundary equilibria and the positive equilibrium is addressed,respectively.Therefore,the sufficient conditions are given for the permanence and extinction of the model.

关 键 词：生态-流行病模型 阶段结构 时滞 稳定性 HOPF分支 

分 类 号：O175.1[理学—数学]