带有2类时滞的传染病竞争模型的稳定性与Hopf分支  

Stability and Hopf Bifurcation Analysis on A Predator-prey Model with Discrete and Distributed Delays and Disease in the Prey

作　　者：黄利航[1] 黄建科 郭云霞[1] 

机构地区：[1]空军工程大学理学院,陕西西安710051 [2]西安陆军学院科学文化基础教研室,陕西西安710108

出　　处：《宁夏大学学报（自然科学版）》2013年第3期193-198,共6页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11171201)

摘　　要：研究了一类带有2类时滞的传染病竞争模型.利用Routh-Hurwitze判据,首先研究时滞为0时系统的稳定性,接着研究时滞竞争系统正平衡点局部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 compete model with disease in the prey. By analyzing discrete and distributed delays is investigated, where the model with the associated characteristic equation and Routh-Hurwitz conditions, the stable condition of the prey-free model is obtained. Then, choosing the delays as a bifurcation parameter the paper shows that the equation exhibits the Hopf bifurcation. By using the method of literature the length of the delay to preserve the stability and the switching stability around equilibrium can be given. Numerical experiments support the 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]