对等网络中被动型蠕虫传播动力学建模与分析

鉴于被动型蠕虫对网络的安全构成了威胁,考虑网络异质性和一次搜索允许的跳数,提出一个带有补充率和移除率的新动力学模型,推导出决定被动型蠕虫能否传播的阈值--基本再生数,分析了无蠕虫平衡点和正平衡点的稳定性问题。最后通过数值模拟验证了理论的正确性,并对参数敏感性进行了分析。研究结果发现,当基本再生数大于1时,跳数的增加不但加快被动型蠕虫的传播,而且使感染节点的数量也增加;当基本再生数小于1时,跳数的增加使感染节点的数量迅速减少,最终被动型蠕虫灭绝。

Dynamical Modeling and Analysis of Passive Worms Propagation in P2P Networks

Passive worms pose a threat to the security of the network. In this paper, considering network heterogeneity and the number of hops a search can reach, a novel dynamical model with recruitment rate and removal rate is proposed. The threshold, the basic reproduction number, is derived, which decides whether passive worms can spread. And the stabili-ties of the worm-free equilibrium and positive equilibrium are analyzed. Finally, the correctness of the theory is verified by numerical simulation, and the sensitivity of parameters is analyzed. The results show that if the basic reproduction number is greater than 1, the propagation speed of passive worms is accelerated with the increase of hop count, which increases the number of infected nodes. If the basic reproduction number is less than 1, the number of infected nodes decreases rapidly with the increase of hop count and passive worms are extinct eventually.