Global stability for a SEIQR worm propagation model in mobile internet

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-08-19 DOI:10.1515/ijnsns-2021-0186

L. Zhang, Pengyan Liu

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Abstract

Abstract Recently, propagation models of worms in the mobile environment are drawing extensive attention, particularly in the Wi-Fi scenario. Considering that worm-free equilibrium is exponential convergent means that the propagation time and control time of worms are much shorter than for other asymptotic convergence. Besides, the global asymptotic stability of the endemic equilibrium is more important than the local asymptotic stability, which reflects the more global qualitative behavior of the worm propagation. In this paper, we discuss the global dynamics of SEIQR worm propagation model in mobile internet proposed by Xiao et al. [X. Xiao, P. Fu, C. Dou, Q. Li, G. Hu, and S. Xia, “Design and analysis of SEIQR worm propagation model in mobile internet,” Commun. Nonlinear Sci. Numer. Simulat., vol. 43, pp. 341–350, 2017] to improve and complement the related results. Through a series of mathematical derivations, sufficient conditions are derived to ensure the global exponentially stability of worm-free equilibrium, and the exponential convergent rate can be unveiled. Then, by using the classical geometric approach, it is shown that the endemic equilibrium is globally asymptotically stable and the system is persistent when R 0 > 1. Moreover, numerical simulations are given to demonstrate our theoretical results.

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移动互联网中SEIQR蠕虫传播模型的全局稳定性

近年来，蠕虫在移动环境下的传播模式受到了广泛关注，尤其是在Wi-Fi场景下。考虑无虫平衡是指数收敛的，意味着蠕虫的传播时间和控制时间比其他渐近收敛的情况要短得多。此外，地方性平衡的全局渐近稳定性比局部渐近稳定性更重要，反映了蠕虫传播的全局定性行为。本文讨论了Xiao等人提出的移动互联网中SEIQR蠕虫传播模型的全局动态。肖平，傅平，窦晨，李强，胡国光，夏生，“移动互联网中SEIQR蠕虫传播模型的设计与分析”，通信学报。非线性科学。号码。装病者。[中文]，vol. 43, pp. 341-350, 2017]以完善和补充相关结果。通过一系列数学推导，得到了保证无虫平衡全局指数稳定的充分条件，并揭示了指数收敛速率。然后，利用经典的几何方法，证明了当R为0时，系统的局部平衡点是全局渐近稳定的，系统是持久的。通过数值模拟验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.