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Modeling and Hopf Bifurcation Analysis of Benign Worms with Quarantine Strategy

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Part of the book series:Lecture Notes in Computer Science ((LNSC,volume 10581))

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Abstract

Since the Morris worm occurred in 1988, malwares have threatened the network persistently. With rapid development of the Internet, network security issues become increasingly serious. Recently, the benign worms become a new active countermeasure to deal with the worm threat. In this paper, we propose a compositive-hybrid benign worm propagation model with quarantine strategy. Usually, quarantine strategy will lead to a time delay, and the worm propagation system will be unstable and out of control with the time delay increases. Then the existence condition and the stability of the positive equilibrium are derived. Through our derivation and analysis, the threshold\( \tau_{0} \) of Hopf bifurcation is obtained. The system will be stable when time delay\( \tau < \tau_{0} \). In addition, numerical experiments are performed and the effect of benign worms is displayed by comparing with the model that do not include benign worms. Furthermore, simulation experiments are carried out to verify our conclusions.

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Acknowledgments

This paper is supported by Program for Fundamental Research Funds of the Central Universities under Grant no. N150402006 and N161704005.

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Authors and Affiliations

  1. Key Laboratory of Medical Image Computing of Ministry of Education, Northeastern University, Shenyang, 110004, China

    Yu Yao, Qiang Fu, Chuan Sheng & Wei Yang

  2. College of Compute Science and Engineering, Northeastern University, Shenyang, 110819, China

    Yu Yao, Qiang Fu & Chuan Sheng

  3. Software College, Northeastern University, Shenyang, 110819, China

    Wei Yang

Authors
  1. Yu Yao

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  2. Qiang Fu

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  3. Chuan Sheng

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  4. Wei Yang

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Corresponding authors

Correspondence toYu Yao orQiang Fu.

Editor information

Editors and Affiliations

  1. Deakin University , Geelong, China

    Sheng Wen

  2. Fujian Normal University, Fuzhou Shi, China

    Wei Wu

  3. University of Salerno, Fisciano, Italy

    Aniello Castiglione

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Yao, Y., Fu, Q., Sheng, C., Yang, W. (2017). Modeling and Hopf Bifurcation Analysis of Benign Worms with Quarantine Strategy. In: Wen, S., Wu, W., Castiglione, A. (eds) Cyberspace Safety and Security. CSS 2017. Lecture Notes in Computer Science(), vol 10581. Springer, Cham. https://doi.org/10.1007/978-3-319-69471-9_24

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