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| 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 |
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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.
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Received: 07 August 2015
Published: 01 March 2016
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| Fund: Supported by Anhui Provincial Natural Science Foundation (1608085QF145, 1608085QF151,KJ2014A006). |
一类具有临时免疫的时滞蠕虫传播模型的Hopf分支
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
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