一类时滞网络病毒传播模型的Hopf分支  

Hopf Bifurcation of Delayed Computer Virus Propagation Model

作　　者：宋磊[1] 王春雷[2] 

机构地区：[1]武汉市妇女儿童医疗保健中心信息科,湖北武汉430014 [2]湖北医药学院网络中心,湖北十堰442000

出　　处：《计算机与现代化》2016年第11期79-82,共4页Computer and Modernization

基　　金：湖北医药学院研究生启动基金资助项目(2011QDZR-24)

摘　　要：考虑到杀毒软件查杀病毒需要一定的时间周期,以及免疫主机对网络病毒的临时免疫力,本文基于SIQR网络病毒传播模型提出一类时滞SIQRS网络病毒传播模型。以杀毒软件查杀病毒需要一定的时间周期时滞为分支参数,通过分析相应特征方程根的分布,得到模型有病毒平衡点局部渐近稳定和产生Hopf分支的充分条件。给出一个仿真示例,对理论分析结果的正确性进行了验证。Considering that anti-virus software needs a period to clean viruses and there is a temporary immunity for the recovered computers, a delayed computer virus propagation model based on the SIQR computer virus propagation model is proposed. Suffi- cient conditions for local stability of the positive equilibrium and occurrence of a Hopf bifurcation are obtained by regarding the delay as a bifurcation parameter and analyzing the distribution of the roots of the associated characteristic equation. Finally, a nu- merical simulation example is carried out to support the theoretical predictions.

关 键 词：时滞 HOPF分支 SIQRS模型 稳定性 

分 类 号：TP309.5[自动化与计算机技术—计算机系统结构]