【摘要】 基于潜伏计算机具有感染病毒的可能性,以及多时滞的计算机病毒研究更加能体现病毒传播情况的一般性.建立一类双时滞的SLIR计算机病毒模型,考虑感染节点重装系统和杀毒软件清除潜伏节点都需要一定的时间周期.首先,分析模型在两种不同类型下特征根的情况,以时滞作为参数,讨论模型在病毒平衡点处的局部渐近稳定性,Hopf分岔的存在性.其次,应用中心流形定理和规范形定理,研究Hopf分岔的方向,分岔周期解的稳定性.最后,通过数值仿真验证结果的正确性.更多还原

【Abstract】 Based on the possibility that latent computers can infect viruses,and the research of computer viruses with delays can reflect the generality of virus transmission. A SLIR computer virus model with two delays is investigated. It takes a certain time period to consider the infected node reinstallation system and the antivirus software to clear the latent nodes. Firstly,the local asymptotic stability of the model at the virus equilibrium point and the existence of Hopf bifurcation are discussed with time delay as the parameter. Secondly,the direction of Hopf bifurcation and the stability of periodic solutions are studied by using the central manifold theorem and the normal form theorem. Finally,numerical simulation is prescented to show the correctness of the results.更多还原