摘要
基于传染病动力学理论,建立了具有自发行为的SIRI谣言传播微分方程动力学模型,通过非负平衡点的存在性给出影响谣言传播效果的阈值.利用Jacobian矩阵和Bendixson-Dulac判别法分析了非负平衡点的全局稳定性,提出了影响谣言传播的主要因素及治理谣言的策略.理论证明,自发行为存在是谣言传播的必要条件,当阈值大于1时,谣言持续,否则谣言灭绝.数值仿真为理论结果提供了支持.复杂的动力学性质表明,该模型对参数的变化非常敏感,对控制和治理谣言传播起了重要作用.
Based on the theory of epidemic dynamics,a dynamic SIRI model of differential equation about rumor spreading with spontaneous behavior was established.By analyze the existence of non-negative equilibria,the threshold which effect the rumor spreading result is determined.Jacobian matrix and bendixson-dulac discriminant method were used to analyze the stability of the non-negative equilibria.Furthermore,the main factors affecting the rumor spreading and the strategies in order to control rumor spreading are given.The theoretical analysis shows that the existence of spontaneous behavior is a necessary condition for rumor spreading.If the threshold is more than 1,the rumor will last,otherwise the rumor will die out.Numerical simulations are provided to support the theoretical results.The complicated dynamics properties exhibit that the model is very sensitive to variation of parameters,which play an important role on controlling and administering the rumor spreading.
作者
刘芳
李明涛
LIU Fang;LI Mingtao(Department of Mathematics,Xinzhou Teachers University,Xinzhou 034000;College of Mathematics,Taiyuan University of Technology,Taiyuan 030024)
出处
《系统科学与数学》
CSCD
北大核心
2020年第7期1257-1269,共13页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金青年项目(11801398)
山西省应用基础研究面上青年项目(201801D221024)
忻州师范学院科研基金项目(2018KY14)资助课题。
