Nonlinear Dynamics of Discrete-Time Model for Computer Virus Propagation: Chaos, Complexity, Stabilization and Synchronization

Ali Aloui (), Imane Zouak, Omar Kahouli, Adel Ouannas, Lilia El Amraoui and Mohamed Ayari ()
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Ali Aloui: Department of Electronics Engineering, Applied College, University of Ha’il, P.O. Box 2440, Ha’il 81451, Saudi Arabia
Imane Zouak: System Dynamics and Control Laboratory, Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Omar Kahouli: Department of Electronics Engineering, Applied College, University of Ha’il, P.O. Box 2440, Ha’il 81451, Saudi Arabia
Adel Ouannas: Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Lilia El Amraoui: Department of Electrical Engineering, College of Engineering, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Mohamed Ayari: Department of Information Technology, Faculty of Computing and Information Technology, Northern Border University, Arar 91431, Saudi Arabia

Mathematics, 2025, vol. 13, issue 22, 1-23

Abstract: This paper investigates a discrete-time compartmental model for computer virus propagation. The model classifies computers into susceptible, latent, and breaking-out states, with nonlinear dynamics driven by infection, recovery, and breakout processes. Stability is analyzed using the basic reproduction number R 0 , and chaotic behavior is demonstrated through phase portraits, bifurcation diagrams, and maximum Lyapunov exponents. To further characterize complexity, the C 0 complexity measure is computed, confirming the richness of the chaotic regime. In addition, control strategies are designed to stabilize the dynamics, and a master–slave synchronization scheme is proposed and validated. Numerical simulations highlight both the complexity and controllability of the system, underscoring its relevance for understanding and mitigating the propagation of computer viruses.

Keywords: discrete-time model; computer virus; stability; chaos; C 0 complexity; stabilisation; synchronization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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