Dynamics and intermittent stochastic stabilization of a rumor spreading model with guidance mechanism in heterogeneous network

• Published in: Chinese physics B Vol. 31; no. 4; pp. 40205 - 120
• Main Authors: Zhong, Xiaojing, Yang, Yukun, Miao, Runqing, Peng, Yuqing, Liu, Guiyun
• Format: Journal Article
• Language: English
• Published: Chinese Physical Society and IOP Publishing Ltd 01.03.2022; School of Mechanical and Electrical Engineering,Guangzhou University,Guangzhou 510006,China%College of Arts and Sciences,Beijing Normal University at Zhuhai,Zhuhai 519087,China
• Subjects: aperiodically intermittent stochastic stabilization; global dynamic analysis; guidance mechanism; heterogenous network; global dynamic analysis; guidance mechanism; aperiodically intermittent stochastic stabilization; heterogenous network
• ISSN: 1674-1056
• DOI: 10.1088/1674-1056/ac587d

We propose a novel rumor propagation model with guidance mechanism in heterogeneous complex networks. Firstly, the sharp threshold of rumor propagation, global stability of the information-equilibrium and information-prevailing-equilibrium under R 0 < 1 and R 0 > 1 is carried out by Lyapunov method and LaSalle’s invariant principle. Next, we design an aperiodically intermittent stochastic stabilization method to suppress the rumor propagation. By using the Itô formula and exponential martingale inequality, the expression of the minimum control intensity is calculated. This method can effectively stabilize the rumor propagation by choosing a suitable perturb intensity and a perturb time ratio, while minimizing the control cost. Finally, numerical examples are given to illustrate the analysis and method of the paper.