Dynamics of a controlled discontinuous computer worm system

Li, Wenjie; Ji, Jinchen; Huang, Lihong

doi:10.1090/proc/15095

Dynamics of a controlled discontinuous computer worm system
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by Wenjie Li, Jinchen Ji and Lihong Huang

Proc. Amer. Math. Soc. 148 (2020), 4389-4403

DOI: https://doi.org/10.1090/proc/15095

Published electronically: June 30, 2020

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Abstract:

This paper studies the dynamic behaviour of a computer worm system under a discontinuous control strategy. Some conditions for globally asymptotically stable solutions of the discontinuous system are obtained by using the Bendixson–Dulac theorem, Green’s formula, and the Lyapunov function. It is found that the solutions of the controlled computer worm system can converge to either of two local equilibrium points or the sliding equilibrium point on the discontinuous surface. It is shown that a threshold control strategy can effectively control the spread of computer viruses. The research results may be applicable to control other types of virus systems.

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