广义网络上的计算机病毒传播模型

摘要/Abstract

摘要：

为了研究计算机病毒在广义网络中传播的机制，文章分别提出了计算机病毒传播的非线性和线性模型.理论分析表明，网络的最大特征值是决定计算机病毒传播的重要参数.其次，文章给出非线性和线性模型中的无病毒均衡点全局稳定的充分条件，同时也证明了线性模型的有病毒平衡点的全局吸引性.最后，通过一些数学模拟实验验证了理论分析的主要结论.

关键词: 计算机病毒, 传播模型, 广义网络, 全局性态, 数值分析

Abstract:

To explore the mechanism that computer viruses spread on generalized networks, this paper proposes a novel nonlinear and a novel linear computer viruses propagation models. Theoretical analysis demonstrates that the maximum eigenvalue of the network is a vital parameter determining the computer viruses propagation. Then, the global stability of virus-free equilibriums in both nonlinear and linear models has been proved. The global attractivity of the viral equilibrium of the linear model has also been proved. Eventually, some numerical simulation results verify the main conclusions of the theoretical analysis.

Key words: Computer Virus, Propagation Model, Generalized Networks, Global Behavior, Numerical Analysis

中图分类号:

O193

张春明,陈冬垚. 广义网络上的计算机病毒传播模型[J]. 数学物理学报, 2019, 39(2): 402-416.

Chunming Zhang,Dongyao Chen. Propagation of Computer Virus on Generalized Networks[J]. Acta mathematica scientia,Series A, 2019, 39(2): 402-416.

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