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浙江大学学报(理学版)  2016, Vol. 43 Issue (3): 279-285    DOI: 10.3785/j.issn.1008-9497.2016.03.005
数学与计算机科学     
一类具有临时免疫的时滞蠕虫传播模型的Hopf分支
张子振, 毕殿杰, 赵涛
安徽财经大学 管理科学与工程学院, 安徽 蚌埠 233030
Delay induced Hopf bifurcation in a worm propagation model with partial immunization
ZHANG Zizhen, BI Dianjie, ZHAO Tao
School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, Anhui Province, China
 全文: PDF(361 KB)  
摘要: 研究一类具有临时免疫的时滞SVEIR网络蠕虫传播模型的Hopf分支.首先,以蠕虫病毒的潜伏期时滞为分支参数,得到Hopf分支存在的充分条件.然后,借助于规范型理论和中心流形定理研究了模型Hopf分支的性质.最后,给出仿真示例,验证所得理论结果的正确性.仿真结果表明,延迟Hopf分支的产生可以有效控制蠕虫病毒在网络中的传播.
关键词: SVEIR模型Hopf分支时滞稳定性周期解    
Abstract: This paper is devoted to Hopf bifurcation of a delayed SVEIR model with partial immunization that describes worms propagation on internet. Sufficient conditions for existence of Hopf bifurcation are obtained by considering the latent period time delay of worms as the bifurcation parameter. Properties of Hopf bifurcation are then investigated with the help of the normal form theory and the center manifold theorem. Numerical simulations show that worms propagation in internet can be controlled and eliminated by shortening the time delay.
Key words: SVEIR model    Hopf bifurcation    time delay    stability    periodic solutions
收稿日期: 2015-08-07 出版日期: 2016-03-01
CLC:  TP309.5  
作者简介: ZHANG Zizhen(1982-), ORCID:http://orcid-org/0000-0002-2879-4434,male, doctor, lecture, the fields of interest include the network security and the dynamical system, E-mail: zhangzizhen0120@163.com.
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引用本文:

张子振, 毕殿杰, 赵涛. 一类具有临时免疫的时滞蠕虫传播模型的Hopf分支[J]. 浙江大学学报(理学版), 2016, 43(3): 279-285.

ZHANG Zizhen, BI Dianjie, ZHAO Tao. Delay induced Hopf bifurcation in a worm propagation model with partial immunization. Journal of ZheJIang University(Science Edition), 2016, 43(3): 279-285.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.03.005        https://www.zjujournals.com/sci/CN/Y2016/V43/I3/279

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