Chaos, control and synchronization in discrete time computer virus system with fractional orders

Omar Kahouli; Imane Zouak; Ma'mon Abu Hammad; Adel Ouannas; Omar Kahouli; Imane Zouak; Ma'mon Abu Hammad; Adel Ouannas

doi:10.3934/math.2025612

AIMS Mathematics

2025, Volume 10, Issue 6: 13594-13621. doi: 10.3934/math.2025612

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Chaos, control and synchronization in discrete time computer virus system with fractional orders

1.
Department of Electronics Engineering, Applied College, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
System Dynamics and Control Laboratory, Department of Mathematics and Informatics, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria
3.
Department of Mathematics, Al-Zaytoonah University of Jordan, Amman 11733, Jordan
4.
Department of Mathematics and Computer Sciences, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria

Received: 07 March 2025 Revised: 29 May 2025 Accepted: 29 May 2025 Published: 13 June 2025
MSC : 34A08, 37D45, 68M12, 93C55, 93D20

In this research, we present a novel discrete fractional-order model designed to simulate computer virus propagation. We performed a thorough dynamical analysis, encompassing phase portrait visualization, bifurcation diagram construction, maximal Lyapunov exponent computation, and equilibrium point stability assessment using the basic reproduction number ($ R_0 $). To characterize system complexity and validate chaotic dynamics, we employed Approximate Entropy, $ C_0 $ Complexity, and Permutation Entropy. Furthermore, control and synchronization methodologies were developed to mitigate chaotic behavior and achieve coordinated system dynamics. The findings proved the efficacy of the proposed fractional model in accurately simulating viral spread and illustrated the considerable implications of fractional-order parameters on system dynamics. In order to validate the results, MATLAB simulations were run.
- computer viruses dynamics,
- fractional discrete model,
- stability,
- chaos,
- control
Citation: Omar Kahouli, Imane Zouak, Ma'mon Abu Hammad, Adel Ouannas. Chaos, control and synchronization in discrete time computer virus system with fractional orders[J]. AIMS Mathematics, 2025, 10(6): 13594-13621. doi: 10.3934/math.2025612

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Abstract

In this research, we present a novel discrete fractional-order model designed to simulate computer virus propagation. We performed a thorough dynamical analysis, encompassing phase portrait visualization, bifurcation diagram construction, maximal Lyapunov exponent computation, and equilibrium point stability assessment using the basic reproduction number ($ R_0 $). To characterize system complexity and validate chaotic dynamics, we employed Approximate Entropy, $ C_0 $ Complexity, and Permutation Entropy. Furthermore, control and synchronization methodologies were developed to mitigate chaotic behavior and achieve coordinated system dynamics. The findings proved the efficacy of the proposed fractional model in accurately simulating viral spread and illustrated the considerable implications of fractional-order parameters on system dynamics. In order to validate the results, MATLAB simulations were run.

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