基于双极社会强化的谣言传播模型稳定性分析与优化控制  

Stability Analysis and Optimal Control of Rumor Propagation Model Based on Bipolar Social Reinforcement

作　　者：王建荣 关莹[1] WANG Jianrong;GUAN Ying(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China;College of Intelligence and Computing,Tianjin University,Tianjin 300072,China)

机构地区：[1]山西大学数学科学学院,山西太原030006 [2]天津大学智能与计算学部,天津300072

出　　处：《山西大学学报（自然科学版）》2022年第4期968-979,共12页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省高等学校科技创新项目(2020L0021);中国博士后科学基金(2021M692400);江苏省自然科学基金(BK20201479)。

摘　　要：考虑了双极社交强化因素和唤醒机制,建立了一种新颖的ISHR(Ignorants-Spreaders-Hibernator-Recovered)谣言传播动力学模型,利用下一代矩阵理论计算出基本再生数R0,通过构造Lyapunov函数证明了无谣言平衡点和正平衡点的全局稳定性。考虑到媒体对谣言传播的抑制作用,对参数遗忘率δ和失去兴趣率θ进行了最优控制分析,计算得到了一个最优控制解。最后,利用数值模拟对系统的稳定性分析结果进行了验证,对基本再生数R0的相关参数进行了敏感性分析,并对敏感性较强的遗忘率δ和失去兴趣率θ进行了优化控制分析。The bipolar social reinforcement factor and wake-up mechanism are considered,and a novel dynamic model of ISHR(Ignorants-Spreaders-Hibernator-Recovered)rumor propagation is established.We calculate the basic reproduction number R_(0) by the next generation matrix theory,and prove the global stability of rumor-free equilibrium and positive equilibrium by Lyapunov function.Considering the inhibitory effect of media on rumor propagation,the optimal control of forgetting rateδand interest loss rateθis analyzed,and an optimal control solution is obtained.The numerical simulation is used to verify the stability analysis results of the system,and the sensitivity analysis of the relevant parameters of the basic regeneration number R_(0) is carried out.Moreover,the optimal control analysis of the more sensitive forgetting rateδand loss of interest rateθis carried out.

关 键 词：谣言传播 双极社会强化 稳定性分析 基本再生数 优化控制 

分 类 号：O175[理学—数学]