一类时滞SIRS微信信息传播模型稳定性和Hopf分岔

Stability and Hopf Bifurcation of a Delayed SIRSWeChat Information Propagation Model

社交软件微信作为国内普遍使用的沟通联络方式和信息获取渠道,其可能带来的网络安全问题不容忽视。为了了解微信信息的动态传播过程,本文研究了一类时滞SIRS微信信息传播模型,以微信用户对信息的临时免疫期时滞为参数,通过讨论特征根的分布,得到模型局部渐近稳定和产生Hopf分岔的充分条件,进而利用中心流形定理和规范形理论确定了Hopf分岔的方向和分岔周期解的稳定性,最后通过仿真示例验证了理论结果的正确性。

The network security of social software WeChat should not be ignored,since it is commonly used as a communication and information acquisition channel in China.In order to understand the dynamic propagation process of WeChat information,this paper studies a kind of SIRS WeChat information propagation model with time delay.The model takes the We-Chat user's temporary immunization period lag as a parameter.By discussing the distribution of the feature root,the model is locally asymptotically stable.The sufficient conditions for Hopf bifurcation are generated.Then the central manifold theorem and normative theory are used to determine the direction of Hopf bifurcation and the stability of bifurcation periodic solution.Finally,the correctness of the theoretical results is verified by simulation examples.