REN Wei1, SONG Li-peng1, FENG Li-ping2
(1. School of Computer and Control Engineering, North University of China, Taiyuan 030051, China;2. Department of Computer Science and Technology, Xinzhou Teachers University, Xinzhou 034000, China)
Abstract： Peer-to-Peer (P2P) botnet has emerged as one of the most serious threats to Internet security. To effectively eliminate P2P botnet, a delayed SEIR model is proposed，which can portray the formation process of P2P botnet. Then, the local stability at equilibria is carefully analyzed by considering the eigenvalues’ distributed ranges of characteristic equations. Both mathematical analysis and numerical simulations show that the dynamical features of the proposed model rely on the basic reproduction number and time delay τ. The results can help us to better understand the propagation behaviors of P2P botnet and design effective counter-botnet methods.
Key words： Peer-to-Peer (P2P) botnet; stability; SEIR model; time delay
CLD number： TP393.08 Document code： A
Article ID： 1674-8042(2014)04-0062-06 doi： 10.3969/j.issn.1674-8042.2014.04.012
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僵尸网络的新型数学模型
任玮1, 宋礼鹏1, 冯丽萍2
(1. 中北大学 计算机与控制工程学院， 山西 太原 030051； 2. 忻州师范学院 计算机科学与技术系， 山西 忻州 034000)
摘要:P2P 僵尸网络已成为互联网安全领域最严重的威胁之一。 为了有效地遏制P2P僵尸网络， 本文提出刻画 P2P 僵尸网络形成过程的一种新模型， 该模型是带时滞的 SEIR 模型。 基于特征方程特征值的分布范围， 分析了模型在平衡点的局部稳定性。 理论分析和数值模拟结果都表明， 该时滞模型的动力学特征依赖于基本再生数 R0 和时间延迟 τ。 本文的结果有助于更好地了解 P2P 僵尸网络的传播行为， 并据此设计有效的反制措施。
关键词:P2P 僵尸网络； 稳定性； SEIR 模型； 时滞
引用格式：REN Wei, SONG Li-peng, FENG Li-ping. A novel mathematical model on Peer-to-Peer botnet. Journal of Measurement Science and Instrumentation, 2014, 5(4): 62-67. [doi: 10.3969/j.issn.1674-8042.2014.04.012]
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