具有时滞的生态-流行病SI模型的稳定性和Hopf分支及其数值模拟  

Stability and Hopf Bifurcation of an Eco-epidemiological SI Model with Delays and Numerical Simulation

作　　者：赵红妮[1] 窦霁虹[1] 

机构地区：[1]西安思源学院,西安710038

出　　处：《江西科学》2015年第6期788-794,共7页Jiangxi Science

基　　金：陕西省教育厅自然科学专项基金(11JK0511)

摘　　要：考虑一类含有时滞的食饵染病的生态-流行病SI模型,主要利用特征根法讨论了平衡点的存在性及其稳定性,证明了当时滞τ<τ_0时,正平衡点是局部渐近稳定的,随着时滞增加,正平衡点由稳定变为不稳定,系统在正平衡点附近产生Hopf分支,通过数值模拟表明正平衡点的性质与理论分析一致。A delayed SI predator-prey epidemiological system with disease spreading in prey population is considered in this paper. Using the method of characteristic equation the existence and stability of the equilibria are analyzed. Positive equilibrium is locally asymptotically stable when time delayτ 〈 τ0. While a loss of stability by a Hopf bifurcation can occur as the delays increase. the results are showed by numerical simulation that the qualities of the positive equilibrium are in accordance with the theory analysis.

关 键 词：生态-流行病模型 渐近稳定 HOPF分支 

分 类 号：O175.12[理学—数学]