Lyapunov functions for studying global asymptotic stability of two rumor spreading models

作     者：Manh Tuan Hoang Manh Tuan Hoang

作者机构：Department of MathematicsFPT UniversityHoa Lac Hi-Tech ParkKm29 Thang Long BlvdHanoiVietnam 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2023年第75卷第10期

页      面：155-165页

核心收录：

学科分类：050302[文学-传播学] 05[文学] 07[理学] 070104[理学-应用数学] 0503[文学-新闻传播学] 0701[理学-数学] 

基　　金：We would like to thank the editor and anonymous referees for useful and valuable comments that led to a great improvement of the paper 

主　　题：rumor propagation models global asymptotic stability Lyapunov stability theory control strategies social networks 

摘      要：In a previous work(2018,***.70,795–802),a new compartment model for the spreading of rumors was introduced and ***,only the local asymptotic stability of this model was *** the present work,we first provide a rigorous mathematical analysis for the global asymptotic stability(GAS)of the above-mentioned rumor spreading *** constructing suitable Lyapunov candidate functions,we obtain the GAS of a rumor-free(boundary)equilibrium point and a unique rumor-spreading(positive)equilibrium *** that,we utilize the approach based on the Lyapunov candidate functions to study the GAS of another rumor spreading model with control strategies,which was proposed in(2022,Physica A 606,128157).As an important consequence,the GAS of the rumor spreading model with control strategies is determined fully without resorting to technical hypotheses used in the benchmark ***,the theoretical findings are supported by a set of illustrative numerical *** obtained results not only improve the ones constructed in the two abovementioned benchmark papers but also can be extended to study the global dynamics of other rumor propagation models in the context of both integer-order and fractional-order derivatives.