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具有饱和发病率的超ILSR谣言传播模型的动力学分析

Dynamical Analysis of Hyper-ILSR Rumor Propagation Model with Saturation Incidence Rate.

作者信息

Mei Xuehui, Zhang Ziyu, Jiang Haijun

机构信息

College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China.

出版信息

Entropy (Basel). 2023 May 16;25(5):805. doi: 10.3390/e25050805.

DOI:10.3390/e25050805
PMID:37238560
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10216982/
Abstract

With the development of the Internet, it is more convenient for people to obtain information, which also facilitates the spread of rumors. It is imperative to study the mechanisms of rumor transmission to control the spread of rumors. The process of rumor propagation is often affected by the interaction of multiple nodes. To reflect higher-order interactions in rumor-spreading, hypergraph theories are introduced in a Hyper-ILSR (Hyper-Ignorant-Lurker-Spreader-Recover) rumor-spreading model with saturation incidence rate in this study. Firstly, the definition of hypergraph and hyperdegree is introduced to explain the construction of the model. Secondly, the existence of the threshold and equilibrium of the Hyper-ILSR model is revealed by discussing the model, which is used to judge the final state of rumor propagation. Next, the stability of equilibrium is studied by Lyapunov functions. Moreover, optimal control is put forward to suppress rumor propagation. Finally, the differences between the Hyper-ILSR model and the general ILSR model are shown in numerical simulations.

摘要

随着互联网的发展，人们获取信息更加便捷，这也为谣言的传播提供了便利。研究谣言传播机制以控制谣言传播势在必行。谣言传播过程往往受到多个节点相互作用的影响。为了反映谣言传播中的高阶相互作用，本研究在一个具有饱和发生率的超无知-潜伏者-传播者-恢复（Hyper-ILSR）谣言传播模型中引入了超图理论。首先，引入超图和超度的定义来解释模型的构建。其次，通过对模型的讨论揭示了Hyper-ILSR模型阈值和平衡点的存在性，用于判断谣言传播的最终状态。接下来，利用李雅普诺夫函数研究平衡点的稳定性。此外，提出了最优控制来抑制谣言传播。最后，通过数值模拟展示了Hyper-ILSR模型与一般ILSR模型之间的差异。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/704245417bc9/entropy-25-00805-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/e40a20a2d288/entropy-25-00805-g002.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/b45ee12c92f2/entropy-25-00805-g005a.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/1eb86b92302f/entropy-25-00805-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/77ebcf1bad79/entropy-25-00805-g007a.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/700bed265831/entropy-25-00805-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/704245417bc9/entropy-25-00805-g009.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/e40a20a2d288/entropy-25-00805-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/0d55319d3086/entropy-25-00805-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/5d30e195de87/entropy-25-00805-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/c0a53e57d702/entropy-25-00805-g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/b45ee12c92f2/entropy-25-00805-g005a.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/1eb86b92302f/entropy-25-00805-g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/77ebcf1bad79/entropy-25-00805-g007a.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/700bed265831/entropy-25-00805-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/6ae8/10216982/704245417bc9/entropy-25-00805-g009.jpg

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Dynamic Analysis and Optimal Control of Rumor Spreading Model with Recurrence and Individual Behaviors in Heterogeneous Networks.异构网络中具有递归和个体行为的谣言传播模型的动态分析与最优控制
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