多语言环境下具有惩罚机制和时滞的谣言传播动力学研究

任静静; 梅雪晖; 罗续鹏; 常忠雪

doi:10.13568/j.cnki.651094.651316.2022.10.13.0002

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多语言环境下具有惩罚机制和时滞的谣言传播动力学研究

更新时间：2026-01-23

- 多语言环境下具有惩罚机制和时滞的谣言传播动力学研究
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 40, Issue 3, Pages: 292-304(2023)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2022.10.13.0002
  CLC： O175;G206
- Published：2023
- 稿件说明：
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[1]任静静,梅雪晖,罗续鹏,等.多语言环境下具有惩罚机制和时滞的谣言传播动力学研究[J].新疆大学学报(自然科学版)(中英文),2023,40(03):292-304+312.
[1]任静静,梅雪晖,罗续鹏,等.多语言环境下具有惩罚机制和时滞的谣言传播动力学研究[J].新疆大学学报(自然科学版)(中英文),2023,40(03):292-304+312. DOI： 10.13568/j.cnki.651094.651316.2022.10.13.0002.

DOI：10.13568/j.cnki.651094.651316.2022.10.13.0002.

摘要

提出了一种多语言环境下带有惩罚机制和时滞的谣言传播优化控制模型.首先

通过分析平均场方程推导出模型的基本再生数R0.其次

基于Routh-Hurwitz判据、Lyapunov方法和LaSalle不变原理

研究了无谣言/谣言盛行平衡点的存在性和稳定性.同时

为了有效地控制谣言传播和控制成本

提出了带有惩罚机制的最优控制.最后

通过数值模拟验证了理论结果的有效性.

Abstract

This paper proposes an optimal control model for rumor propagation with punishment mechanism and time delay in a multi-lingual environment. Firstly

the basic reproduction number R0 of the model is derived by analyzing the mean field equation. Secondly

based on Routh-Hurwitz judgment

Lyapunov method and LaSalle invariant principle

the existence and stability of rumor-free/rumor-prevailing equilibrium are studied. At the same time

in order to control costs and effectively control the spread of rumors

optimal control with the punishment mechanism is proposed. Finally

the validity of the theoretical results are verified by numerical simulations.

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references

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