Dynamic properties of rumor propagation model induced by Lévy noise on social networks

doi:10.1088/1674-1056/ad58c5

Abstract Social networks are inevitably subject to disruptions from the physical world, such as sudden internet outages that sever local connections and impede information flow. While Gaussian white noise, commonly used to simulate stochastic disruptions, only fluctuates within a narrow range around its mean and fails to capture large-scale variations, Lévy noise can effectively compensate for this limitation. Therefore, a susceptible-infected-removed rumor propagation model with Lévy noise is constructed on homogeneous and heterogeneous networks, respectively. Then, the existence of a global positive solution and the asymptotic path-wise of the solution are derived on heterogeneous networks, and the sufficient conditions of rumor extinction and persistence are investigated. Subsequently, theoretical results are verified through numerical calculations and the sensitivity analysis related to the threshold is conducted on the model parameters. Through simulation experiments on Watts-Strogatz (WS) and Barabási-Albert networks, it is found that the addition of noise can inhibit the spread of rumors, resulting in a stochastic resonance phenomenon, and the optimal noise intensity is obtained on the WS network. The validity of the model is verified on three real datasets by particle swarm optimization algorithm.

Keywords: rumor propagation model Lévy noise extinction and persistence stochastic resonance

Received: 25 March 2024
Revised: 02 June 2024
Accepted manuscript online: 17 June 2024

PACS:	02.50.Ey	(Stochastic processes)
	02.50.Fz	(Stochastic analysis)
	64.60.aq	(Networks)
	87.23.Kg	(Dynamics of evolution)

Fund: Acknowledgements This work is supported in part by the National Natural Science Foundation of China (Grant Nos. 62071248 and 62201284) and in part by the Graduate Scientific Research and Innovation Program of Jiangsu Province (Grant No. KYCX24_1119).

Corresponding Authors: Youguo Wang
E-mail: wangyg@njupt.edu.cn

Cite this article:

Ying Jing(景颖), Youguo Wang(王友国), Qiqing Zhai(翟其清), and Xianli Sun(孙先莉) Dynamic properties of rumor propagation model induced by Lévy noise on social networks 2024 Chin. Phys. B 33 090203

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