两类网络蠕虫的建立与动力学分析

发布时间：2018-04-10 15:36

本文选题：网络蠕虫 + 数学模型　；参考：《中北大学》2014年硕士论文

【摘要】：由于网络蠕虫具有传播速度快、传播形式复杂多样、破坏性大的特点，计算机网络蠕虫已经成为互联网络上最为严重的安全威胁之一。如何有效防御网络蠕虫成为迫切需要解决的网络问题。网络蠕虫之间存在着复杂的关系，因此需提出有效的措施防御网络蠕虫。本文对依靠移动设备传播的网络蠕虫和网络蠕虫之间相互关系及防御措施进行了分析研究。首先在多板块中研究依靠移动设备传播的网络蠕虫，并针对其特殊性建立了相应的数学模型。在一个板块中，通过分析模型得到阈值条件，无病平衡点和正平衡点存在性，并分析其稳定性；在多板块中分析已达到稳态的板块对未感染板块的影响，并给出相应的防御措施，如提高移动设备的安全使用率阻止其网络蠕虫入侵计算机。最后通过数值模拟验证了理论分析结果。其次网络蠕虫之间由于存在着复杂的关系，，其对网络蠕虫的传播和演变等动力学行为有着重要的影响，分析这些关系有助于找到更好的控制和防御策略。建立了两类蠕虫传播的数学模型，通过计算分析得到两个阈值条件，无病平衡点，两个边界平衡点及惟一正平衡点的存在性。通过理论分析可以得到要控制网络蠕虫可以通过控制参数来实现，进一步给出控制网络蠕虫相对应的措施。最后通过数值模拟验证了理论分析结果。最后建立了两类相互竞争的网络蠕虫传播的数学模型，通过分析得到两个阈值条件及无病平衡点，并证明无病平衡点的局部渐近稳定性，得到网络蠕虫存在的条件，并分析两类蠕虫同时持续存在的条件。
[Abstract]:Because the network worm has the characteristics of fast propagation, complex and diverse forms of transmission, and great destruction, the computer network worm has become one of the most serious security threats on the Internet.How to effectively defend against network worms has become an urgent network problem to be solved.There are complex relationships between network worms, so it is necessary to propose effective measures to defend against network worms.In this paper, the relationship between network worms and network worms spread by mobile devices and their defense measures are analyzed and studied.Firstly, the network worm propagating by mobile devices is studied in multi-plate, and the corresponding mathematical model is established according to its particularity.In a plate, the threshold condition is obtained by analyzing the model, the existence and stability of disease-free equilibrium point and positive equilibrium point are analyzed, and the influence of the plate that has reached steady state on the uninfected plate is analyzed in multiple plates.The corresponding defense measures are given, such as increasing the security utilization rate of mobile devices to prevent their network worms from invading the computer.Finally, the theoretical analysis results are verified by numerical simulation.Secondly because of the complex relationship between the network worms it has an important impact on the propagation and evolution of the network worm dynamic behavior. The analysis of these relationships will help to find better control and defense strategies.Two kinds of mathematical models of worm propagation are established, and the existence of two threshold conditions, disease-free equilibrium point, two boundary equilibrium points and the unique positive equilibrium point are obtained by calculation and analysis.Through the theoretical analysis, it can be concluded that the network worm can be controlled by controlling parameters, and the corresponding measures for controlling the network worm are given.Finally, the theoretical analysis results are verified by numerical simulation.Finally, two kinds of mathematical models of competing network worm propagation are established. By analyzing two threshold conditions and disease-free equilibrium points, the local asymptotic stability of disease-free equilibrium points is proved, and the conditions for the existence of network worms are obtained.At the same time, the condition that two kinds of worms persist at the same time is analyzed.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TP393.08

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