带有两类时滞的传染病-捕食模型的稳定性与Hopf分支研究  

Stability and Hopf bifurcation analysis on a epidemic-predator model with discrete and distributed delays

作　　者：黄利航[1] 赵惠文[1] 杨亚莉[1] 

机构地区：[1]空军工程大学理学院,陕西西安710051

出　　处：《福州大学学报（自然科学版）》2014年第3期346-352,共7页Journal of Fuzhou University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11071256);陕西省自然科学基金资助项目(2012JQ1019)

摘　　要：研究一类被捕食者染病且具有离散以及连续两类时滞的捕食与被捕食模型.利用Routh-Hurwitze判据研究时滞为零时系统的稳定性,接着研究时滞捕食系统正平衡点局部Hopf分支存在的条件.根据已知文献中的方法计算系统正平衡点稳定开关的存在性以及时滞长度,最后进行数值模拟.A predatorprey model with discrete and distributed delays is investigated, where themodel with disease in the prey. By analyzing the associated characteristic equation and Routh - Hur-witz conditions, we can obtained the stable condition of the prey - free model. Then, choosing thedelays as a bifurcation parameter this paper show that the equation exhibits the Hopf bifurcation. Byusing the method of literature the length of the delay to preserve the stability and the switching stabilityaround equilibrium can given. Numerical experiments support our theoretical analysis.

关 键 词：时滞 捕食模型 局部渐近稳定 HOPF分支 周期解 

分 类 号：O175.13[理学—数学]