同质网络中具有时滞的谣言传播模型的动力学分析  

Dynamic Analysis of Rumor Propagation Model with Time Delay in Homogeneous Networks

作　　者：童新如 蒋海军[1,2] 陈向勇 TONG Xinru;JIANG Haijun;CHEN Xiangyong(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China;School of Mathematics and Statistics,Yili Normal University,Yining Xinjiang 835000,China;School of Automation and Electrical Engineering,Linyi University,Linyi Shandong 276005,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017 [2]伊犁师范大学数学与统计学院,新疆伊宁835000 [3]临沂大学自动化与电气工程学院,山东临沂276005

出　　处：《新疆大学学报（自然科学版）（中英文）》2022年第6期663-670,共8页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金(62163035,62173175);新疆应用数学自治区重点实验室项目(XJDX1401);中央指导的地方科技发展专项(ZYYD2022A05)。

摘　　要：综合考虑谣言复发、复发时滞以及个体行为因素,建立了同质网络中具有时滞的SHILR(易感者-犹豫者-传播者-潜伏者-恢复者)谣言传播模型.首先,基于平均场方程和下一代矩阵法,给出了模型的基本再生数.其次,利用Lyapunov方法和LaSalle不变原理分析了模型平衡点的全局渐近稳定性.此外,还讨论了时滞对谣言传播的影响.最后,给出数值模拟的实例来验证理论结果.Considering the rumor recurrence,time delay and individual behaviors comprehensively,a novel SHILR(Susceptible-Hesitating-Infected-Latent-Recovered)rumor propagation model with time delay is established in homogeneous networks.Firstly,the basic reproduction number of the model is obtained based on the mean field equation and the next generation matrix method.Secondly,the global asymptotic stabilities of the equilibria are analyzed through applying Lyapunov method and LaSalle’s invariance principle.Additionally,the influence of time delay on rumor propagation is also discussed.Finally,some numerical simulation examples are given to verify the correctness of the theoretical results.

关 键 词：谣言复发 个体行为 同质网络 时滞 稳定性 谣言传播 

分 类 号：O175[理学—数学]