基于元胞自动机与赋权网络模型的病毒传播研究
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摘要
随着网络的不断普及和发展,各种计算机病毒通过互联网也被迅速的传播开来。病毒的广泛传播对计算机网络安全造成了极大威胁。认识病毒传播的特征与规律,并在此基础上对其进行有效的防御和控制将是反病毒研究的重要课题。考虑到现实网络的极其复杂性和覆盖范围之广以及病毒传播的危害性,使得我们在研究基于网络平台的计算机病毒传播时,只好借助于模拟仿真技术进行。这就面临着两个问题：其一是如何对现实网络进行模拟仿真,其二是如何模拟网络上的病毒传播规律。并且对复杂网络的仿真是研究病毒传播的基础。只有在完成了对网络仿真的前提下,才能开展对病毒传播的研究。
过去人们主要研究无权网络上的病毒传播行为,然而现实网络往往呈现出赋权性质,因此对赋权网络上的病毒传播行为进行研究更有意义。本文基于赋权网络模型和元胞自动机方法对赋权网络中的病毒传播演化行为进行了深入研究。主要研究工作包括以下几个方面：
(1)为了反映病毒传播时更加全面微观的网络拓扑结构的动力学演化行为,本文在已有的网络建模研究基础上,构建了一个病毒传播赋权网络模型。此模型改变了原有的单一连接选择机制,提出了一种优先与随机相结合的连接选择新机制,从而使得节点间的连接方式扩展为两种；它增加了内部节点间连边的消亡对网络演化行为的影响,从节点的增加和删除,边的增加和删除这四个局部事件出发,使其不仅能够反映权值动态增加对拓扑演化的影响,而且还能够反映边权值的动态减少对网络演化的影响,从而能更真实的反映现实网络的演化过程。
(2)在病毒传播赋权网络模型的基础上,针对节点间联系越紧密,被感染的概率越大这一现象,对以往无权网络中的感染机制进行了拓展,提出了一种基于邻居感染权重的微观感染机制。
(3)为了能更好的反映局部微观下病毒传播时节点间相互作用的动力学演化行为,利用元胞自动机的方法,在(1)和(2)研究成果的基础上,构建了一个病毒传播的元胞自动机模型。元胞自动机模型结构灵活,能够在演化过程中改变控制策略,研究各因素对病毒传播的影响,从而有效地克服了利用平均场方法构建的微分方程模型只能反映病毒传播大致趋势的局限性。
(4)同时考虑到网络动力学和节点动力学对病毒传播的影响,通过对病毒传播的机制与动力学进行分析,使得病毒传播的赋权网络模型和元胞自动机模型有机结合起来,从节点状态演化和网络拓扑演化两方面,对时变的动态网络拓扑结构下的病毒传播过程进行微观模拟。实验首先验证了本文所提的赋权网络模型的适用性和正确性,在此基础上对病毒传播进行模拟。并通过改变参数c和d,分析了不同的网络拓扑结构对病毒传播的影响,得出网络非均匀性越强,将能加快病毒的传播；通过改变感染概率p和康复概率β,研究了不同传播参数对病毒传播的影响,得出减小p值,增大β值能有效减小病毒的传播范围和感染程度：通过调整用户反应时间f1,得出了缩短ft可以有效的遏制病毒的大规模蔓延。最后根据实验的分析讨论结果,给出了相关病毒防治建议。
With the development and popularization of network, varieties of computer viruses have quickly spread through the Internet. Its widespread formed a great threat to the whole computer network security. It will be an important subject of anti-virus research to defense and control viruses based on understanding their characteristics and laws. Considering the practical extreme complexity, wide covering scope of network and harms of virus spread, it had to use simulation technology when we research computer virus spread which based on the network platform. And here come two questions. One is how to simulate the practical network, while the other is how to simulate the law of virus spread on the network. What's more, the research of virus spread is based on simulation of the complex network. Only when completing the network simulation, can the research on virus spread be made.
In the past, people mainly studied the virus spreading behavior in the un-weighted network. However, most of the practical networks often show weighted property, so it is more meaningful to research the virus spreading behavior in weighted networks. This paper made profound research on virus spreading behavior in weighted networks based on the weighted network model and cellular automata method. The research work mainly included the following aspects:
(1) In order to reflect the dynamic evolution behavior of more comprehensive and microcosmic network topology structure, this paper established a virus spreading model in weighted network. This model changed the original single connection selection, and advanced a new connection selection mechanism combining partial priority and randomness, which made the connection of nodes in two ways. It increased the influence on the network evolution behavior when the connection border of inner nodes died out. Starting from four partial affairs of nodes'increasing and deleting, borders'increasing and deleting, it not only can reflect the influence of weight value's dynamic increasing on topology evolution, but also can reflect the influence of border weight value's decreasing on network evolution, so that it can reflect the evolution process of practical network more factually.
(2) Based on the virus spread weighted network model, in allusion to the phenomenon that the denser nodes are, larger ratio to be infected, it expanded the infection mechanism in un-weighted network, and put forward a micro infection mechanism based on neighbor infection weight.
(3) In order to better reflect the dynamic evolution behavior of interaction among nodes when virus spread in partial microcosmic, it constructed a cellular automata model of virus spread, using cellular automata method on the basis of the former two research achievement. The cellular automata model has flexible structure, and can change controlling strategy in the evolution process, study the influence of each factor on virus spread, so that can effectively conquer the limitation that the differential equation constructed by average field method can only reflect the general trend of virus spread.
(4) Considering the influence of network dynamics and node dynamics on virus spread, through analysis of virus spread mechanism and dynamics, this paper organically combined the weighted network model and cellular automata model of virus spread, and made micro simulation of virus spread process under time-varying dynamic network topology structure from nodes status evolution and network topology evolution. The experiment proved the applicability and correctness of weighted network mode advanced in this paper, and then simulated the virus spread. Through changing parameter c and d, it analyzed the influence of different network topology structures on virus spread. Through changing the infection ratio P and recovery ratioβ, it studied the influence of different spreading parameters on virus spread, and got the conclusion that the decreasing of p and increasing ofβcan effectively reduce the viruses'spreading distance and infection degree. Through adjusting the user's reaction time ft, it showed that the shortening of ft could effectively check viruses'extensive overspread. Finally, according to the analyzing discussion and conclusion of experiment, this paper put forward the suggestion to prevent viruses.
过去人们主要研究无权网络上的病毒传播行为,然而现实网络往往呈现出赋权性质,因此对赋权网络上的病毒传播行为进行研究更有意义。本文基于赋权网络模型和元胞自动机方法对赋权网络中的病毒传播演化行为进行了深入研究。主要研究工作包括以下几个方面：
(1)为了反映病毒传播时更加全面微观的网络拓扑结构的动力学演化行为,本文在已有的网络建模研究基础上,构建了一个病毒传播赋权网络模型。此模型改变了原有的单一连接选择机制,提出了一种优先与随机相结合的连接选择新机制,从而使得节点间的连接方式扩展为两种；它增加了内部节点间连边的消亡对网络演化行为的影响,从节点的增加和删除,边的增加和删除这四个局部事件出发,使其不仅能够反映权值动态增加对拓扑演化的影响,而且还能够反映边权值的动态减少对网络演化的影响,从而能更真实的反映现实网络的演化过程。
(2)在病毒传播赋权网络模型的基础上,针对节点间联系越紧密,被感染的概率越大这一现象,对以往无权网络中的感染机制进行了拓展,提出了一种基于邻居感染权重的微观感染机制。
(3)为了能更好的反映局部微观下病毒传播时节点间相互作用的动力学演化行为,利用元胞自动机的方法,在(1)和(2)研究成果的基础上,构建了一个病毒传播的元胞自动机模型。元胞自动机模型结构灵活,能够在演化过程中改变控制策略,研究各因素对病毒传播的影响,从而有效地克服了利用平均场方法构建的微分方程模型只能反映病毒传播大致趋势的局限性。
(4)同时考虑到网络动力学和节点动力学对病毒传播的影响,通过对病毒传播的机制与动力学进行分析,使得病毒传播的赋权网络模型和元胞自动机模型有机结合起来,从节点状态演化和网络拓扑演化两方面,对时变的动态网络拓扑结构下的病毒传播过程进行微观模拟。实验首先验证了本文所提的赋权网络模型的适用性和正确性,在此基础上对病毒传播进行模拟。并通过改变参数c和d,分析了不同的网络拓扑结构对病毒传播的影响,得出网络非均匀性越强,将能加快病毒的传播；通过改变感染概率p和康复概率β,研究了不同传播参数对病毒传播的影响,得出减小p值,增大β值能有效减小病毒的传播范围和感染程度：通过调整用户反应时间f1,得出了缩短ft可以有效的遏制病毒的大规模蔓延。最后根据实验的分析讨论结果,给出了相关病毒防治建议。
With the development and popularization of network, varieties of computer viruses have quickly spread through the Internet. Its widespread formed a great threat to the whole computer network security. It will be an important subject of anti-virus research to defense and control viruses based on understanding their characteristics and laws. Considering the practical extreme complexity, wide covering scope of network and harms of virus spread, it had to use simulation technology when we research computer virus spread which based on the network platform. And here come two questions. One is how to simulate the practical network, while the other is how to simulate the law of virus spread on the network. What's more, the research of virus spread is based on simulation of the complex network. Only when completing the network simulation, can the research on virus spread be made.
In the past, people mainly studied the virus spreading behavior in the un-weighted network. However, most of the practical networks often show weighted property, so it is more meaningful to research the virus spreading behavior in weighted networks. This paper made profound research on virus spreading behavior in weighted networks based on the weighted network model and cellular automata method. The research work mainly included the following aspects:
(1) In order to reflect the dynamic evolution behavior of more comprehensive and microcosmic network topology structure, this paper established a virus spreading model in weighted network. This model changed the original single connection selection, and advanced a new connection selection mechanism combining partial priority and randomness, which made the connection of nodes in two ways. It increased the influence on the network evolution behavior when the connection border of inner nodes died out. Starting from four partial affairs of nodes'increasing and deleting, borders'increasing and deleting, it not only can reflect the influence of weight value's dynamic increasing on topology evolution, but also can reflect the influence of border weight value's decreasing on network evolution, so that it can reflect the evolution process of practical network more factually.
(2) Based on the virus spread weighted network model, in allusion to the phenomenon that the denser nodes are, larger ratio to be infected, it expanded the infection mechanism in un-weighted network, and put forward a micro infection mechanism based on neighbor infection weight.
(3) In order to better reflect the dynamic evolution behavior of interaction among nodes when virus spread in partial microcosmic, it constructed a cellular automata model of virus spread, using cellular automata method on the basis of the former two research achievement. The cellular automata model has flexible structure, and can change controlling strategy in the evolution process, study the influence of each factor on virus spread, so that can effectively conquer the limitation that the differential equation constructed by average field method can only reflect the general trend of virus spread.
(4) Considering the influence of network dynamics and node dynamics on virus spread, through analysis of virus spread mechanism and dynamics, this paper organically combined the weighted network model and cellular automata model of virus spread, and made micro simulation of virus spread process under time-varying dynamic network topology structure from nodes status evolution and network topology evolution. The experiment proved the applicability and correctness of weighted network mode advanced in this paper, and then simulated the virus spread. Through changing parameter c and d, it analyzed the influence of different network topology structures on virus spread. Through changing the infection ratio P and recovery ratioβ, it studied the influence of different spreading parameters on virus spread, and got the conclusion that the decreasing of p and increasing ofβcan effectively reduce the viruses'spreading distance and infection degree. Through adjusting the user's reaction time ft, it showed that the shortening of ft could effectively check viruses'extensive overspread. Finally, according to the analyzing discussion and conclusion of experiment, this paper put forward the suggestion to prevent viruses.
引文
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