基于有向网络的Email病毒传播模型及其震荡吸引子研究

Study of directed networks-based Email virus propagation model and its concussion attractor

基于有向Email网络和Email病毒传播特点,运用平均场方法建立Email病毒传播的时滞微分方程模型,研究Email病毒在有向网络中的震荡传播行为.理论上给出了震荡解的全局吸引子存在的充要条件,数值实验验证了吸引子的存在性和控制.研究表明,子图之间的传播概率决定吸引子的存在性,而有效传播率影响吸引子的振幅,因此这两个参数对于有效预测和控制Email病毒在网络上的传播规模具有重要意义.

According to directed Emall networks and the spread characteristics of Emall virus, we study the behavior of the virus shock propagation in Email networks by using the mean field method to build delay differential equation model of viral spread. Then, the sufficient condition about the existence of shock solution＇s global attractor is given in theory. The existence and control of attractor are proved by numerical experiments. Our research indicates that spread probability between subgraphs determines the existence of attractor, and effective rate of spread determines the amplitude of attractor. Therefore these two parameters are significant in prediction of the scale of viral spread in networks.