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Stability and Hopf bifurcation for a delayed SLBRS computer virus model
1School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China ; Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China.
Thescientificworldjournal
|September 10, 2014
Summary
This study introduces a delayed Susceptible-Latent-Burnt-Removed (SLBRS) computer virus model. Analyzing the model reveals how time delays impact virus dynamics, including stability and bifurcations.
Area of Science:
- Computer Virology
- Mathematical Modeling
- Network Security
Background:
- Computer viruses pose significant threats to digital systems.
- Existing models like SLBRS often do not account for crucial time delays.
- Understanding virus propagation dynamics is essential for effective defense strategies.
Purpose of the Study:
- To propose a novel delayed SLBRS computer virus model.
- To analyze the local stability and Hopf bifurcation of the proposed model.
- To investigate the influence of time delays on computer virus dynamics.
Main Methods:
- Incorporation of time delay into the SLBRS model.
- Analysis of local stability using established mathematical techniques.
- Application of normal form method and center manifold theory for Hopf bifurcation analysis.
Main Results:
- The proposed delayed SLBRS model exhibits complex dynamical behaviors.
- Local stability conditions are determined with respect to the time delay.
- The direction and stability of Hopf bifurcations are analytically derived.
Conclusions:
- Time delays play a critical role in the dynamics of computer viruses.
- The study provides a theoretical framework for understanding virus spread with delays.
- Analytical results are validated through a numerical example, confirming the model's predictive capability.
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