Bifurcation in a delayed worm propagation model with birth and death rates

Yu Yao, N. Zhang, Fu-xiang Gao, Ge Yu
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Abstract

In this paper, a delayed worm propagation model with birth and death rates is discussed. The number of system reinstallations may be increased when the hosts get unstable (infected or quarantined). In view of such situation, dynamic birth and death rates are introduced. Afterwards, the stability of the positive equilibrium is studied. Through the theoretical analysis, it is proved that the model is locally asymptotically stable without time delay. Moreover, a bifurcation appears when time delay t passes a constant value which means that the worm propagation system is unstable and uncontrollable. Thus, the time delay should be decreased in order to predict or eliminate the worm propagation. Finally, a numeric simulation is presented which fully supports our analysis.
具有出生率和死亡率的延迟蠕虫传播模型的分岔
本文讨论了一类具有出生率和死亡率的延迟蠕虫传播模型。当主机变得不稳定(被感染或被隔离)时,系统重新安装的次数可能会增加。鉴于这种情况,引入了动态出生率和死亡率。然后,对正平衡的稳定性进行了研究。通过理论分析,证明了该模型是局部无时滞渐近稳定的。当时滞t超过一定值时,出现分叉,说明蠕虫传播系统不稳定,不可控。因此,为了预测或消除蠕虫传播,应该减少时间延迟。最后,给出了一个数值模拟,完全支持了我们的分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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