具有时滞和饱和接触率的SIRS模型的Hopf分支  

Hopf bifurcation of SIRS models with delayed and saturation incidence

作　　者：章培军[1] 王震[1] 孙卫[1] 张慧[2] ZHANG Peijun;WANG Zhen;SUN Wei;ZHANG Hui(Department of Applied Statistics and Science, Xijing University, Xi’an 710123, China;Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China)

机构地区：[1]西京学院应用统计与理学系,西安710123 [2]西北工业大学应用数学系,西安710072

出　　处：《计算机工程与应用》2016年第17期68-72,共5页Computer Engineering and Applications

基　　金：国家自然科学基金(No.10971164);陕西省自然科学基础研究计划项目(No.2016JM1024);陕西省教育厅科研计划项目(No.15JK2181);西京学院科研基金项目(No.XJ160143)

摘　　要：应用微分方程分支理论,研究了具有时滞和饱和接触率的SIRS模型,以时滞τ为分支参数,运用Hopf分支理论,得到当时滞τ充分小时正平衡点是局部渐近稳定的,当τ经过一系列临界值时模型出现Hopf分支。用Matlab软件进行数值仿真验证了结论的正确性。This thesis researches SIRS models with delayed and saturation incidence by using the bifurcation method of differential equations. By means of the Hopf bifurcation theorem and considering the delay τ as a bifurcation parameter,the endemic equilibrium is locally stable when τ is small enough and Hopf bifurcation occurs when τ passes through some critical values. Matlab is employed to carry out numerical simulation to verify the results.

关 键 词：时滞 HOPF分支 饱和接触率 SIRS模型 

分 类 号：O175[理学—数学] Q141[理学—基础数学]