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

作　　者：Manh Tuan Hoang 

机构地区：[1]Department of Mathematics,FPT University,Hoa Lac Hi-Tech Park,Km29 Thang Long Blvd,Hanoi,Vietnam

出　　处：《Communications in Theoretical Physics》2023年第10期155-165,共11页理论物理通讯（英文版）

摘　　要：In a previous work(2018,Commun.Theor.Phys.70,795–802),a new compartment model for the spreading of rumors was introduced and analyzed.However,only the local asymptotic stability of this model was discussed.In the present work,we first provide a rigorous mathematical analysis for the global asymptotic stability(GAS)of the above-mentioned rumor spreading model.By constructing suitable Lyapunov candidate functions,we obtain the GAS of a rumor-free(boundary)equilibrium point and a unique rumor-spreading(positive)equilibrium point.After 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 work.Lastly,the theoretical findings are supported by a set of illustrative numerical examples.The 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.

关 键 词：rumor propagation models global asymptotic stability Lyapunov stability theory control strategies social networks 

分 类 号：O17[理学—数学]